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2 nd Semester Final Exam Data: 1. MC worth 100 pts. No curve. Class Ave: 58% 2. FR worth 100 pts. No curve. Class Ave: 75% Ch9 Test Data: _________ No.

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Presentation on theme: "2 nd Semester Final Exam Data: 1. MC worth 100 pts. No curve. Class Ave: 58% 2. FR worth 100 pts. No curve. Class Ave: 75% Ch9 Test Data: _________ No."— Presentation transcript:

1 2 nd Semester Final Exam Data: 1. MC worth 100 pts. No curve. Class Ave: 58% 2. FR worth 100 pts. No curve. Class Ave: 75% Ch9 Test Data: _________ No curve. (Prompt + 2 other ?’s have extra credit)

2 AP test sign ups: 1. MC worth 100 pts. + 25pts XC. Class Ave: 58% = 83% 2. FR worth 100 pts. + 25pts XC. Class Ave: 75% = 100% Ch9 Test Data: _________ Still no curve. (Prompt + 2 other ?’s have extra credit)

3 Ch9 Test:

4 Ch10.1 – Elasticity and Oscillations Hooke’s Law ∆F= -k(∆x)

5 Ch10.1 – Elasticity and Oscillations Hooke’s Law ∆F= -k(∆x) Ex1) A 9.0 cm long spring is suspended from a hook. A 20g mass is attached and it stretches to 10cm. A 40g mass is attached and it stretches to 15.5cm. A 50g mass is attached and it stretches to 18.5cm. a. Please graph F vs. x b. Find the spring constant 2 ways 1.0 F (N) distance (cm)

6 Ex1) A 9.0 cm long spring is suspended from a hook. A 20g mass is attached and it stretches to 10cm. A 40g mass is attached and it stretches to 15.5cm. A 50g mass is attached and it stretches to 18.5cm. a. Please graph F vs. x b. Find the spring constant 2 ways = =.1 c. How far will the spring stretch to if a 100g mass is attached? d. How much work is done by the spring to stretch it to 18.5 cm? 1.0 F (N) distance (cm)

7 Ex1) A 9.0 cm long spring is suspended from a hook. A 20g mass is attached and it stretches to 10cm. A 40g mass is attached and it stretches to 15.5cm. A 50g mass is attached and it stretches to 18.5cm. a. Please graph F vs. x b. Find the spring constant 2 ways c. How far will the spring stretch to if a 100g mass is attached? d. How much work is done by the spring to stretch it to 18.5 cm? 1.0 F (N) distance (cm)

8 Ex1) A 9.0 cm long spring is suspended from a hook. A 20g mass is attached and it stretches to 10cm. A 40g mass is attached and it stretches to 15.5cm. A 50g mass is attached and it stretches to 18.5cm. a. Please graph F vs. x b. Find the spring constant 2 ways 1 2 c. How far will the spring stretch to if a 100g mass is attached? d. How much work is done by the spring to stretch it to 18.5 cm? 1.0 F (N) distance (cm)

9 Potential Energy stored in a spring: PE s = ½k(∆x) 2 (FRQ later, on chapter test, and on final exam!)

10 Ch10.2 – Simple Harmonic Motion (notes to speed up tomorrow) - object oscillates in a continuous pattern, under the influence of simple forces. - the periodic motion of the object can be graphed as a sine or cosine wave. Period - time it takes to complete 1 cycle. (T) Frequency - # of cycles completed per second (hertz) Angular frequency (ω) - rotations per second Ex1) A wheel completes one revolution every 2.5 seconds. What is its angular frequency? Ch10 HW#1 p374 1,3,6,8,9,11

11 1. A helical spring 20-cm long extends to a length of 25 cm when it supports a load of 50 N. Determine the spring constant. 3. A steel spring is suspended vertically from its upper end and a monkey weighing 10.0 N grabs hold of its bottom end and hangs motionlessly from it. If the elastic constant of the spring is 500 N/m, by how much will the monkey stretch it? 6. A long metal wire hangs from the roof truss in a factory building. A 1000-kg machine is attached to it so that the load is suspended above the floor. If the wire stretches cm, what is the k?

12 Ch10 HW#1 p374 1,3,6,8,9,11 1. A helical spring 20-cm long extends to a length of 25 cm when it supports a load of 50 N. Determine the spring constant. 3. A steel spring is suspended vertically from its upper end and a monkey weighing 10.0 N grabs hold of its bottom end and hangs motionlessly from it. If the elastic constant of the spring is 500 N/m, by how much will the monkey stretch it? 6. A long metal wire hangs from the roof truss in a factory building. A 1000-kg machine is attached to it so that the load is suspended above the floor. If the wire stretches cm, what is the k?

13 Ch10 HW#1 p374 1,3,6,8,9,11 1. A helical spring 20-cm long extends to a length of 25 cm when it supports a load of 50 N. Determine the spring constant. 3. A steel spring is suspended vertically from its upper end and a monkey weighing 10.0 N grabs hold of its bottom end and hangs motionlessly from it. If the elastic constant of the spring is 500 N/m, by how much will the monkey stretch it? 6. A long metal wire hangs from the roof truss in a factory building. A 1000-kg machine is attached to it so that the load is suspended above the floor. If the wire stretches cm, what is the k?

14 Ch10 HW#1 p374 1,3,6,8,9,11 1. A helical spring 20-cm long extends to a length of 25 cm when it supports a load of 50 N. Determine the spring constant. 3. A steel spring is suspended vertically from its upper end and a monkey weighing 10.0 N grabs hold of its bottom end and hangs motionlessly from it. If the elastic constant of the spring is 500 N/m, by how much will the monkey stretch it? 6. A long metal wire hangs from the roof truss in a factory building. A 1000-kg machine is attached to it so that the load is suspended above the floor. If the wire stretches cm, what is the k?

15 8.How much energy is stored in a spring with an elastic constant pf 50 N/m when compressed 0.05 m? 9. A helical spring is 55-cm long when a load of 100 N is hung from it and 57- cm long when the load is 110 N. Find its spring constant. 11. A Hookean spring is suspended vertically and a mass of 2.00 kg is hung from its end. The spring then stretches 10.0 cm. How much more will it elongate if an additional 0.50 kg is attached to the first mass? First find k:Then find new ∆x:

16 8.How much energy is stored in a spring with an elastic constant pf 50 N/m when compressed 0.05 m? 9. A helical spring is 55-cm long when a load of 100 N is hung from it and 57- cm long when the load is 110 N. Find its spring constant. 11. A Hookean spring is suspended vertically and a mass of 2.00 kg is hung from its end. The spring then stretches 10.0 cm. How much more will it elongate if an additional 0.50 kg is attached to the first mass? First find k:Then find new ∆x:

17 8.How much energy is stored in a spring with an elastic constant pf 50 N/m when compressed 0.05 m? 9. A helical spring is 55-cm long when a load of 100 N is hung from it and 57- cm long when the load is 110 N. Find its spring constant. 11. A Hookean spring is suspended vertically and a mass of 2.00 kg is hung from its end. The spring then stretches 10.0 cm. How much more will it elongate if an additional 0.50 kg is attached to the first mass? First find k:Then find new ∆x:

18 8.How much energy is stored in a spring with an elastic constant pf 50 N/m when compressed 0.05 m? 9. A helical spring is 55-cm long when a load of 100 N is hung from it and 57- cm long when the load is 110 N. Find its spring constant. 11. A Hookean spring is suspended vertically and a mass of 2.00 kg is hung from its end. The spring then stretches 10.0 cm. How much more will it elongate if an additional 0.50 kg is attached to the first mass? First find k:Then find new ∆x:

19 Ch10.2 – Simple Harmonic Motion - object oscillates in a continuous pattern, under the influence of simple forces. - the periodic motion of the object can be graphed as a sine or cosine wave. Period - time it takes to complete 1 cycle. (T) Frequency - # of cycles completed per second (hertz)

20 Ch10.2 – Simple Harmonic Motion (notes to speed up tomorrow) - object oscillates in a continuous pattern, under the influence of simple forces. - the periodic motion of the object can be graphed as a sine or cosine wave. Period - time it takes to complete 1 cycle. (T) Frequency - # of cycles completed per second (hertz) Angular frequency (ω) - rotations per second Ex1) A wheel completes one revolution every 2.5 seconds. What is its angular frequency?

21 Ch10.2 – Simple Harmonic Motion - object oscillates in a continuous pattern, under the influence of simple forces. - the periodic motion of the object can be graphed as a sine or cosine wave. Period - time it takes to complete 1 cycle. (T) Frequency - # of cycles completed per second (hertz) Angular frequency (ω) - rotations per second Ex1) A wheel completes one revolution every 2.5 seconds. What is its angular frequency? T = 2.5sec

22 Different springs = diff oscillations (diff spring constants) Each has its own natural frequency, ω. Sine waveCosine wave or

23 Different springs = diff oscillations (diff spring constants) Each has its own natural frequency, ω. Sine waveCosine wave Period x = A. sinωt x = A. cosωtor or

24 Ex2) A 1 N bird lands on a branch that bends and goes into SHM with a period of.5 sec. Determine the effective elastic spring constant for the branch.

25 k=? F g = 1N T = 0.5sk = 15.6N/m

26 Ex3) A 1 kg cart is attached to a spring and pulled back with a force of 10N a distance of 5 cm, as shown. a) What is the value of the spring constant? b) What is the period of oscillation? d) Where will the cart be.20s after release. c) Write an equation to represent it’s motion.

27 Ex3) A 1 kg cart is attached to a spring and pulled back with a force of 10N a distance of 5 cm, as shown. a) What is the value of the spring constant? b) What is the period of oscillation? d) Where will the cart be.20s after release. c) Write an equation to represent it’s motion.

28 Ex3) A 1 kg cart is attached to a spring and pulled back with a force of 10N a distance of 5 cm, as shown. a) What is the value of the spring constant? b) What is the period of oscillation? d) Where will the cart be.20s after release. c) Write an equation to represent it’s motion.

29 Ex3) A 1 kg cart is attached to a spring and pulled back with a force of 10N a distance of 5 cm, as shown. a) What is the value of the spring constant? b) What is the period of oscillation? d) Where will the cart be.20s after release. c) Write an equation to represent it’s motion.

30 Ex3) A 1 kg cart is attached to a spring and pulled back with a force of 10N a distance of 5 cm, as shown. a) What is the value of the spring constant? b) What is the period of oscillation? d) Where will the cart be.20s after release. c) Write an equation to represent it’s motion. e) At what time will it pass thru the equilibrium position?

31 Ex3) A 1 kg cart is attached to a spring and pulled back with a force of 10N a distance of 5 cm, as shown. a) What is the value of the spring constant? b) What is the period of oscillation? d) Where will the cart be.20s after release. c) Write an equation to represent it’s motion. e) At what time will it pass thru the equilibrium position? t =.11s

32 Ex 4) A 2.0 kg bag of candy is hung vertically from a spring that elongates 50 cm under the load, just out of reach of a child. His mean big brother pushes it up 25cm and releases it, setting it in SHM. If the kid can only reach the bag at its lowest point, when will he grab the candy? (Solve 2 ways) Ch10 HW#2 WS

33 Ex 4) A 2.0 kg bag of candy is hung vertically from a spring that elongates 50 cm under the load, just out of reach of a child. His mean big brother pushes it up 25cm and releases it, setting it in SHM. If the kid can only reach the bag at its lowest point, when will he grab the candy? (Solve 2 ways) Ch10 HW#2 WS

34 Ex 4) A 2.0 kg bag of candy is hung vertically from a spring that elongates 50 cm under the load, just out of reach of a child. His mean big brother pushes it up 25cm and releases it, setting it in SHM. If the kid can only reach the bag at its lowest point, when will he grab the candy? (Solve 2 ways) 1 st way:2 nd way: If released from top, gets to bottom in half the period. Ch10 HW#2 WS

35 Lab10.1 – Hooke’s Law and Periodic Motion - due tomorrow - Ch10 HW#2 beginning of period. - Lab HW is to complete the backside of the lab perfectly.

36 Ch10 HW#2 – SHM WS 1. An antique phonograph record is turning uniformly at 78rpm while an ant sitting at rest on its rim is being viewed by a child whose eyes are in the plane of the record. Describe the ant’s motion as seen by the child. What is the frequency of the ant? What is the angular frequency? 78 rot 1 min = 1.3Hz min 60 sec 2. A 1 kg mass is attached to a spring, stretching it 10 cm. a. What is the value of the spring constant? b. If it is pushed up 2 cm, what is the period of its oscillation? c. Write a cosine expression representing its motion.

37 Ch10 HW#2 – SHM WS 1. An antique phonograph record is turning uniformly at 78rpm while an ant sitting at rest on its rim is being viewed by a child whose eyes are in the plane of the record. Describe the ant’s motion as seen by the child. What is the frequency of the ant? What is the angular frequency? 78 rot 1 min = 1.3Hz min 60 sec 2. A 1 kg mass is attached to a spring, stretching it 10 cm. a. What is the value of the spring constant? b. If it is pushed up 2 cm, what is the period of its oscillation? c. Write a cosine expression representing its motion.

38 Ch10 HW#2 – SHM WS 1. An antique phonograph record is turning uniformly at 78rpm while an ant sitting at rest on its rim is being viewed by a child whose eyes are in the plane of the record. Describe the ant’s motion as seen by the child. What is the frequency of the ant? What is the angular frequency? 78 rot 1 min = 1.3Hz min 60 sec 2. A 1 kg mass is attached to a spring, stretching it 10 cm. a. What is the value of the spring constant? b. If it is pushed up 2 cm, what is the period of its oscillation? c. Write a cosine expression representing its motion. a. F = kxb. c. x = (.02)cos[(2π/.63)t] 10N = k(.1m) k = 100N/m

39 3. A body oscillates in SHM according to the equation x = 5.0 cos(0.40t) where each term is in SI units. a. What is the amplitude? b. Period? c. Displacement at t = 2.0 s?

40 3. A body oscillates in SHM according to the equation x = 5.0 cos(0.40t) where each term is in SI units. a. What is the amplitude? b. Period? c. Displacement at t = 2.0 s? a. A = 5mb. c. x = 10.0 cos(0.40(2)) x = 7.0m

41 4. 2kg of potatoes are put on a scale that is displaced 2.50 cm as a result. a. What is the elastic spring constant? b. If the scale is pushed down 2 cm and allowed to oscillate, what will be the frequency of the motion? c. If someone started timing right as the potatoes passed through the equilibrium position, write a sine expression representing this motion.

42 4. 2kg of potatoes are put on a scale that is displaced 2.50 cm as a result. a. What is the elastic spring constant? b. If the scale is pushed down 2 cm and allowed to oscillate, what will be the frequency of the motion? c. If someone started timing right as the potatoes passed through the equilibrium position, write a sine expression representing this motion. a. F = kxb. c. x = (.02)sin[(2π3.18)t] 20N = k(.025m) k = 800N/m

43 5. A light 3.0 m long helical spring hangs vertically from a tall stand. A mass of 1.00 kg is then suspended from the bottom of the spring, which lengthens an additional 50 cm before coming to a new equilibrium config well within its elastic limit. The bob is now pushed up 10cm and is released. a. Write an equation describing the displacement as a function of time. b. Where will the mass be 2.45 sec after its release?

44 5. A light 3.0 m long helical spring hangs vertically from a tall stand. A mass of 1.00 kg is then suspended from the bottom of the spring, which lengthens an additional 50 cm before coming to a new equilibrium config well within its elastic limit. The bob is now pushed up 10cm and is released. a. Write an equation describing the displacement as a function of time. b. Where will the mass be 2.45 sec after its release?

45 6. A 2.5 kg ball is suspended from the ceiling by a long string. Someone taps the ball, setting it into SHM as it swings back and forth with a maximum amplitude of 40 cm and a period of 1.2 sec. a. Write a sine expression representing this motion. b. At what time will the ball be 20 cm behind the equilibrium position? (x = m)

46 6. A 2.5 kg ball is suspended from the ceiling by a long string. Someone taps the ball, setting it into SHM as it swings back and forth with a maximum amplitude of 40 cm and a period of 1.2 sec. a. Write a sine expression representing this motion. b. At what time will the ball be 20 cm behind the equilibrium position? (x = m) t = 0.7sec

47 Ch10.3 – Pendulums

48 A gift from Galileo: F T F net F net =0 where l is the length F T of the string. F g (Mass doesn’t matter) F g

49 Ex1) How long should a pendulum be if it is to have a period of 2.00sec at a location where the accl of gravity is 9.81 m/s 2 ?

50 Ex1) How long should a pendulum be if it is to have a period of 2.00sec at a location where the accl of gravity is 9.81 m/s 2 ? Resonance – objects vibrate at their special resonant frequency. (Go read ur textbook about damping, stress and strain.) Ch10 HW#3 p , 91,93, 95

51 Ch10 HW# ,91,93, What happens to the period of a pendulum if we increase its length 4X longer? 83. What happens to frequency if 4X longer? 84. Period if increase mass by 4X greater? 85. Freq of a pendulum with a length of 10m.

52 Ch10 HW# ,91,93, What happens to the period of a pendulum if we increase its length 4X longer? 83. What happens to frequency if 4X longer? 84. Period if increase mass by 4X greater? 85. Freq of a pendulum with a length of 10m.

53 Ch10 HW# ,91,93, What happens to the period of a pendulum if we increase its length 4X longer? 83. What happens to frequency if 4X longer? 84. Period if increase mass by 4X greater? 85. Freq of a pendulum with a length of 10m.

54 Ch10 HW# ,91,93, What happens to the period of a pendulum if we increase its length 4X longer? 83. What happens to frequency if 4X longer? 84. Period if increase mass by 4X greater? 85. Freq of a pendulum with a length of 10m.

55 Ch10 HW# ,91,93, What happens to the period of a pendulum if we increase its length 4X longer? 83. What happens to frequency if 4X longer? 84. Period if increase mass by 4X greater? 85. Freq of a pendulum with a length of 10m.

56 86. Small lead ball is attached to a 1.00m string. Period? 87. How long a pendulum to have a period of 10s? 88. On distant planet, a 1.00m pendulum has a period of 10s. Accl of gravity? 91. What happens to period of pendulum if go to the moon where g m = 1/6g E ?

57 86. Small lead ball is attached to a 1.00m string. Period? 87. How long a pendulum to have a period of 10s? 88. On distant planet, a 1.00m pendulum has a period of 10s. Accl of gravity? 91. What happens to freq of pendulum if go to the moon where g m = 1/6g E ?

58 86. Small lead ball is attached to a 1.00m string. Period? 87. How long a pendulum to have a period of 10s? 88. On distant planet, a 1.00m pendulum has a period of 10s. Accl of gravity? 91. What happens to freq of pendulum if go to the moon where g m = 1/6g E ?

59 86. Small lead ball is attached to a 1.00m string. Period? 87. How long a pendulum to have a period of 10s? 88. On distant planet, a 1.00m pendulum has a period of 10s. Accl of gravity? 91. What happens to freq of pendulum if go to the moon where g m = 1/6g E ?

60 87. How long a pendulum to have a period of 10s? 88. On distant planet, a 1.00m pendulum has a period of 10s. Accl of gravity? 91. What happens to freq of pendulum if go to the moon where g m = 1/6g E ?

61 93. If the period of a simple pendulum is T, what’s the new period if length increases 50%? 95. A pendulum consists of a 2.00cm diameter lead sphere attached to a frictionless pivot via a very long very light cable. It is to swing from its maximum displacement on one side, to its maximum displacement on the other side in 1.00s. If it’s to do this at a place where the acceleration due to gravity is 9.80m/s 2, how long must the cable be?

62 93. If the period of a simple pendulum is T, what’s the new period if length increases 50%? 95. A pendulum consists of a 2.00cm diameter lead sphere attached to a frictionless pivot via a very long very light cable. It is to swing from its maximum displacement on one side, to its maximum displacement on the other side in 1.00s. If it’s to do this at a place where the acceleration due to gravity is 9.80m/s 2, how long must the cable be?

63 93. If the period of a simple pendulum is T, what’s the new period if length increases 50%? 95. A pendulum consists of a 2.00cm diameter lead sphere attached to a frictionless pivot via a very long very light cable. It is to swing from its maximum displacement on one side, to its maximum displacement on the other side in 1.00s. If it’s to do this at a place where the acceleration due to gravity is 9.80m/s 2, how long must the cable be?

64 Ch10.4 – Springs and Pendulums FRQ’s 1. An ideal spring of unstretched length.20 m is placed horizontally on a frictionless table. One end of the spring is fixed and the other end is attached to a block of mass M = 8.0 kg. The 8.0 kg block is also attached to a massless sting that passes over a small frictionless pulley. A block of mass m = 4.0 kg hangs from the other end of the string. When this system is in equilibrium, the length of the spring is 0.25 m and the 4.0 kg block is 0.70 m above the floor. (a) On the figures below, draw free-body diagrams showing and labeling the forces on each block when the system is in equilibrium. M=8.0 kg m=4.0 kg (b) Calculate the tension in the string. (c) Calculate the force constant of the spring. The string is now cut at point P. (d) Calculate the time taken by the 4.0 kg block to hit the floor. (e) Calculate the frequency of the oscillation of the 8.0 kg block. (f) Calculate the maximum speed attained by the 8.0 kg block.

65 FTFT F gm (b) Calculate the tension in the string. F s F T (c) Calculate the force constant of the spring. The string is now cut at point P. (d) Calculate the time taken by the 4.0 kg block to hit the floor. (e) Calculate the frequency of the oscillation of the 8.0 kg block. (f) Calculate the maximum speed attained by the 8.0 kg block. Ch10 HW#4

66 1. A 0.20 kg mass is sliding on a horizontal, frictionless air track with a speed of 3.0 m/s when it instantaneously hits and sticks to a 1.3 kg mass initially at rest on the track. The 1.3 kg mass is connected to one end of a mass-less spring, which has a spring constant of 100 N/m. The other end of the spring is fixed. (a) Determine the following for the 0.20 kg mass immediately before the impact. i. Its linear momentumii. Its kinetic energy (b) Determine the following for the combined masses immediately after the impact. i. Its liner momentumii. Its kinetic energy After the collision, the two masses undergo simple harmonic motion about their position impact. (c) Determine the amplitude of the harmonic motion (d) Determine the period of the harmonic motion.

67 Ch10 HW#4 1. A 0.20 kg mass is sliding on a horizontal, frictionless air track with a speed of 3.0 m/s when it instantaneously hits and sticks to a 1.3 kg mass initially at rest on the track. The 1.3 kg mass is connected to one end of a mass-less spring, which has a spring constant of 100 N/m. The other end of the spring is fixed. (a) Determine the following for the 0.20 kg mass immediately before the impact. i. Its linear momentumii. Its kinetic energy (b) Determine the following for the combined masses immediately after the impact. i. Its liner momentumii. Its kinetic energy After the collision, the two masses undergo simple harmonic motion about their position impact. (c) Determine the amplitude of the harmonic motion (d) Determine the period of the harmonic motion.

68 Ch10 HW#4 2. A simple pendulum consists of a bob of mass 1.8kg attached to a string of length 2.3m. The pendulum is held at an angle of 30°, as shown. a. On the figure, draw a free-body diagram showing and labeling the forces on the bob. b. Calculate the tension on the string. c. The horizontal string is now cut, and the pendulum swings down. Calculate the period of the pendulum

69 Ch11.1 – Waves Wave – a rhythmic disturbance in a medium. Medium – the stuff the waves propagate thru. (rope, slinky, air, water, tuning fork, etc)

70 Ch11.1 – Waves Wave – a rhythmic disturbance in a medium. Medium – the stuff the waves propagate thru. (rope, slinky, air, water, tuning fork, etc) Two types of waves: 1. Transverse – medium moves up and down as wave energy moves forward. (Exs: ocean, light and all electromagnetic radiation.) y x

71 Ch11.1 – Waves Wave – a rhythmic disturbance in a medium. Medium – the stuff the waves propagate thru. (rope, slinky, air, water, tuning fork, etc) Two types of waves: 1. Transverse – medium moves up and down as wave energy moves forward. (Exs: ocean, light and all electromagnetic radiation.) y Amplitude (A) x 1 wavelength (λ)

72 2. Compressional (longitudinal) – Medium moves back and forth as wave energy moves forward. (Ex: sound)

73 2. Compressional (longitudinal) – Medium moves back and forth as wave energy moves forward. (Ex: sound) compressionrarefaction 1 wavelength vvvvvvvv

74 Velocity of a wave v = λ. f velocity = wavelength x frequency Ex1) What is the speed of light, if red light has a wavelength of 780nm and a frequency of 384 THz?

75 Velocity of a wave v = λ. f velocity = wavelength x frequency Ex1) What is the speed of light, if red light has a wavelength of 780nm and a frequency of 384 THz? v = ? λ = 780x10 -9 m v = λ. f f = 384x10 12 Hz = (780x10 -9 m)(384x10 12 s -1 ) = 3x10 8 m / s

76 Ex2) A kid in a boat watches waves pass by, and times the crests to be 0.5 sec apart. It takes 1.5 sec for a wave to sweep down the length of the 4.5 m boat. What is the period, frequency, and wavelength of the waves?

77 Ex2) A kid in a boat watches waves pass by, and times the crests to be 0.5 sec apart. It takes 1.5 sec for a wave to sweep down the length of the 4.5 m boat. What is the period, frequency, and wavelength of the waves? Takes 0.5s from crest to crest s = 4.5mT = 0.5 sec t = 1.5sec v = λ. f 3 m / s = λ. (2s -1 ) λ = 1.5m

78 Ex3) A wave on a string travels at 1.2 m / s and is represented by: y = (0.02)sin(157x)Find amp, λ, f, T.

79 Ex3) A wave on a string travels at 1.2 m / s and is represented by: y = (0.02)sin(157x)Find amp, λ, f, T. Amp

80 Ex4) A transverse wave on a rope. The distance between peaks is 50cm. A dot of red paint at x=0, y=0. A dot of green paint at x=12.5, y=-4.0. What is the vertical displacement for purple dot at x = 60?

81 Ex4) A transverse wave on a rope. The distance between peaks is 50cm. A dot of red paint at x=0, y=0. A dot of green paint at x=12.5, y=-4.0. What is the vertical displacement for purple dot at x = 60? Ch11 HW#1 p428 2,3,4,8,10,12,13

82 Ch11 HW#1 2,3,4,8,10,12,13 (Do 12 last) 2. A long metal rod is struck by a vibrating hammer in such a way that a compressional wave with a wavelength of 4.3m travels down its length at a speed of 3.5 km / s. What was the frequency of the vibration? 3. An ‘A’ note of 440Hz is played on a violin submerged in a swimming pool at the wedding of two scuba divers. Given that the speed of compression waves In pure water is 1498 m / s, what is the wavelength of that tone?

83 Ch11 HW#1 2. A long metal rod is struck by a vibrating hammer in such a way that a compressional wave with a wavelength of 4.3m travels down its length at a speed of 3.5 km / s. What was the frequency of the vibration? 3. An ‘A’ note of 440Hz is played on a violin submerged in a swimming pool at the wedding of two scuba divers. Given that the speed of compression waves In pure water is 1498 m / s, what is the wavelength of that tone?

84 Ch11 HW#1 2. A long metal rod is struck by a vibrating hammer in such a way that a compressional wave with a wavelength of 4.3m travels down its length at a speed of 3.5 km / s. What was the frequency of the vibration? 3. An ‘A’ note of 440Hz is played on a violin submerged in a swimming pool at the wedding of two scuba divers. Given that the speed of compression waves In pure water is 1498 m / s, what is the wavelength of that tone?

85 4. A wave on a string travels a 10m length in 2.0s. A harmonic disturbance of wavelength 0.50m is then generated on the string. What is its frequency? 8. The speed of a sinusoidal wave is 4.00 m / s and its profile is specified by The compression Determine its period.

86 4. A wave on a string travels a 10m length in 2.0s. A harmonic disturbance of wavelength 0.50m is then generated on the string. What is its frequency? 8. The speed of a sinusoidal wave is 4.00 m / s and its profile is specified by The compression Determine its period.

87 4. A wave on a string travels a 10m length in 2.0s. A harmonic disturbance of wavelength 0.50m is then generated on the string. What is its frequency? 8. The speed of a sinusoidal wave is 4.00 m / s and its profile is specified by The compression Determine its period.

88 10. Write an expression for a profile of a sinusoidal wave traveling in the x-direction at a speed of 10.0 m / s. If it has a frequency of 20Hz and an amplitude In the y-direction of 0.010m. 13. A member of the Vespertilionidea family of bats typically emits a sequence of chirps, wavetrains lasting about 3ms and having a carrier frequecy that varies from 100kHz to about 30kHz. Generally, there is a time between individual chirps of 70ms. Assuming the air speed of one of these wavetrains is 330, how far away can an object be and still be detected without being masked by the next outgoing chirp?

89 10. Write an expression for a profile of a sinusoidal wave traveling in the x-direction at a speed of 10.0 m / s. If it has a frequency of 20Hz and an amplitude In the y-direction of 0.010m. 13. A member of the Vespertilionidea family of bats typically emits a sequence of chirps, wavetrains lasting about 3ms and having a carrier frequecy that varies from 100kHz to about 30kHz. Generally, there is a time between individual chirps of 70ms. Assuming the air speed of one of these wavetrains is 330, how far away can an object be and still be detected without being masked by the next outgoing chirp? v = 330 m / s f = 30,000 – 100,000Hz t = 0.07sec between chirps

90 10. Write an expression for a profile of a sinusoidal wave traveling in the x-direction at a speed of 10.0 m / s. If it has a frequency of 20Hz and an amplitude In the y-direction of 0.010m. 13. A member of the Vespertilionidea family of bats typically emits a sequence of chirps, wavetrains lasting about 3ms and having a carrier frequecy that varies from 100kHz to about 30kHz. Generally, there is a time between individual chirps of 70ms. Assuming the air speed of one of these wavetrains is 330, how far away can an object be and still be detected without being masked by the next outgoing chirp? s = v. t v = 330 m / s = (330 m / s )(0.07s) f = 30,000 – 100,000Hz = 23.1 m total t = 0.07sec between chirps (Chirp needs to go out and come backs = 11.6 m one way before the next chirp starts.)

91 12. A transverse wave on a beaded string has an amplitude of 2.5cm and a wavelength of 160cm. If at t=0 a life-size photo shows that the height of the wave at x=0 is zero and at x=40cm, the height is +2.5cm. What is its displacement at x=10cm?

92 12. A transverse wave on a beaded string has an amplitude of 2.5cm and a wavelength of 160cm. If at t=0 a life-size photo shows that the height of the wave at x=0 is zero and at x=40cm, the height is +2.5cm. What is its displacement at x=10cm? 2.5 x y = cm

93 Ch11.2 – Wave Properties Wave Speed – the speed of the wave is determined by the properties of the medium, NOT the motion of the source. Reflections 1. Connected to a fixed point: 2. Connected to a moveable point:

94 Ch11.2 – Wave Properties Wave Speed – the speed of the wave is determined by the properties of the medium, NOT the motion of the source. Reflections 1. Connected to a fixed point: reflects 180° out of phase. 2. Connected to a moveable point:

95 Ch11.2 – Wave Properties Wave Speed – the speed of the wave is determined by the properties of the medium, NOT the motion of the source. Reflections 1. Connected to a fixed point: reflects 180° out of phase. 2. Connected to a moveable point: reflects back in phase

96 Sound Waves - need a medium (no sound in a vacuum)

97 Sound Waves - need a medium (no sound in a vacuum) - series of compressions and rarefactions (small pressure changes. A loud sound ~ 10 Pa) Ex1) Most bands tune to A440, a frequency of 440Hz. If the speed of sound in air at room temp is m / s, what is the wavelength?

98 Sound Waves - need a medium (no sound in a vacuum) - series of compressions and rarefactions (small pressure changes. A loud sound ~ 10 Pa) Ex1) Most bands tune to A440, a frequency of 440Hz. If the speed of sound in air at room temp is m / s, what is the wavelength?

99 Superposition of Waves - waves can travel thru the same space - while they overlap, they add together - when they pass, they continue normal Constructive Interference – waves add Destructive Interference – waves subtract

100 Superposition of Waves - waves can travel thru the same space - while they overlap, they add together - when they pass, they continue normal Constructive Interference – waves add Destructive Interference – waves subtract

101 Ex2) Adding complicated waves + = Ch11 HW#2 p429 26,27,28,51,52,53,56 Doppler Effect

102 Ch11 HW#2 p429 26,27,28,51,52,53, identical transverse wave pulses, each traveling at 5 m / s, heading toward each other. Draw the overlap identical transverse wave pulses, each traveling at 5 m / s, heading toward each other. Draw the overlap.

103 Ch11 HW#2 p429 26,27,28,51,52,53, identical transverse wave pulses, each traveling at 5 m / s, heading toward each other. Draw the overlap identical transverse wave pulses, each traveling at 5 m / s, heading toward each other. Draw the overlap.

104 Ch11 HW#2 p429 26,27,28,51,52,53, identical transverse wave pulses, each traveling at 5 m / s, heading toward each other. Draw the overlap identical transverse wave pulses, each traveling at 5 m / s, heading toward each other. Draw the overlap.

105 28. Write an expression for the profile of a transverse harmonic wave with amplitude of 10cm and wavelength 1.2m traveling along a rope. At t=0, x=0, y= In music, the standard A 4 note has a frequency of 440Hz. What are its period and frequency at room temp? 52. A person standing at one side of a playing field on a cold winter night emits a brief yell. The short acoustical wavetrain returns 1.00 sec later, as an echo that Bounced off a distant dormitory. How far away is the building?

106 28. Write an expression for the profile of a transverse harmonic wave with amplitude of 10cm and wavelength 1.2m traveling along a rope. At t=0, x=0, y= In music, the standard A 4 note has a frequency of 440Hz. What are its period and frequency at room temp? 52. A person standing at one side of a playing field on a cold winter night emits a brief yell. The short acoustical wavetrain returns 1.00 sec later, as an echo that Bounced off a distant dormitory. How far away is the building?

107 28. Write an expression for the profile of a transverse harmonic wave with amplitude of 10cm and wavelength 1.2m traveling along a rope. At t=0, x=0, y= In music, the standard A 4 note has a frequency of 440Hz. What are its period and frequency at room temp? f = 440Hz v = 343 m / s T, λ = ? 52. A person standing at one side of a playing field on a cold winter night emits a brief yell. The short acoustical wavetrain returns 1.00 sec later, as an echo that Bounced off a distant dormitory. How far away is the building?

108 28. Write an expression for the profile of a transverse harmonic wave with amplitude of 10cm and wavelength 1.2m traveling along a rope. At t=0, x=0, y= In music, the standard A 4 note has a frequency of 440Hz. What are its period and frequency at room temp? f = 440Hz v = 343 m / s T, λ = ? 52. A person standing at one side of a playing field on a cold winter night emits a brief yell. The short acoustical wavetrain returns 1.00 sec later, as an echo that Bounced off a distant dormitory. How far away is the building?

109 28. Write an expression for the profile of a transverse harmonic wave with amplitude of 10cm and wavelength 1.2m traveling along a rope. At t=0, x=0, y= In music, the standard A 4 note has a frequency of 440Hz. What are its period and frequency at room temp? f = 440Hz v = 343 m / s T, λ = ? 52. A person standing at one side of a playing field on a cold winter night emits a brief yell. The short acoustical wavetrain returns 1.00 sec later, as an echo that Bounced off a distant dormitory. How far away is the building? s = v. t = (331 m / s )(0.5s) = 165.5m

110 53. A string vibrating at 1000Hz produces a sound wave that travels at 344 m / s. How many wavelengths will correspong to 1m? 56. The speed of sound in ether 1 atm) is 976 m / s. What is the wavelength in ether of a tuning fork oscillating at 1000Hz?

111 53. A string vibrating at 1000Hz produces a sound wave that travels at 344 m / s. How many wavelengths will correspong to 1m? f = 1000Hz 0.344m 1 wave v = 344 m / s m λ = ? 56. The speed of sound in ether 1 atm) is 976 m / s. What is the wavelength in ether of a tuning fork oscillating at 1000Hz?

112 53. A string vibrating at 1000Hz produces a sound wave that travels at 344 m / s. How many wavelengths will correspong to 1m? f = 1000Hz 0.344m 1 wave v = 344 m / s m λ = ? 56. The speed of sound in ether 1 atm) is 976 m / s. What is the wavelength in ether of a tuning fork oscillating at 1000Hz? f = 1000Hz v = 976 m / s λ = ?

113 Ch11.3 Standing Waves – Strings Speed of Sound: (Don’t copy this table)(Copy this though) Material (0°C) SpeedSpeed increases with temp Rubber54 m / s v = v 0 + (.6)T Air330 m / s v 0 = m / s Hydrogen1270 m / s Ex) at 20°C, Water1493 m / s v = Aluminum5104 m / s Granite6000 m / s

114 Ch11.3 Standing Waves – Strings Speed of Sound: (Don’t copy this table)(Copy this though) Material (0°C) SpeedSpeed increases with temp Rubber54 m / s v = v 0 + (.6)T Air330 m / s v 0 = m / s Hydrogen1270 m / s Ex) at 20°C, Water1493 m / s v = (20)(.6) Aluminum5104 m / s = 343 m / s Granite6000 m / s

115 Speed of Sound: (Don’t copy this table)(Copy this though) Material (0°C) SpeedSpeed increases with temp Rubber54 m / s v = v 0 + (.6)T Air330 m / s v 0 = m / s Hydrogen1270 m / s Ex) at 20°C, Water1493 m / s v = (20)(.6) Aluminum5104 m / s = 343 m / s Granite6000 m / s Sound Intensity – measured in deciBels - starts at 0 dB, called the threshold of hearing, and goes up in powers of ten. Faintest sound 0 dB (1.0x W/m 2 ) Whisper10 dB Class50 dB10 dB increase ~ twice as loud Stereo80 dB Harley90 dB Concert120 dB Jet140 dB

116 Standing Waves on strings:

117 Fundamental frequency: ½λ fits L λ = 2L 1 st harmonic: Anitnodes 1λ fits L λ = L 2 nd harmonic:Nodes 1½ λ fits L λ = 2/3L 3 rd harmonic: 2λ fits L λ = ½L

118 Ex1) A guitar string is 64 cm long. If the speed of sound is 343 m / s, what is the lowest possible frequency the string can hold? fund freq: Ex2) A 30 Hz wave generator is attached to a 0.75 m string, causing a standing wave pattern, as shown. What is the speed of the waves on the string Ex3) A banjo has a string length of 80 cm. If the speed of the disturbance on the string is 240 m / s, what is the frequency of the 3 rd harmonic?

119 Ex1) A guitar string is 64 cm long. If the speed of sound is 343 m / s, what is the lowest possible frequency the string can hold? fund freq: Ex2) A 30 Hz wave generator is attached to a 0.75 m string, causing a standing wave pattern, as shown. What is the speed of the waves on the string 1 st harmonic: λ = L = 0.75m f = 30Hz Ex3) A banjo has a string length of 80 cm. If the speed of the disturbance on the string is 240 m / s, what is the frequency of the 3 rd harmonic? 3 rd harmonic: λ = ½L = 0.40m v = 15 m / s Ch11 HW#3 1 – 5

120 1. A mandolin string is 105 cm long. If it’s a cold day, the speed of sound is 335 m/s, what is the lowest possible frequency the string can hold? fund freq: ½λ = L ½λ = 1.05m λ = 2.10m 2. A 230 Hz tuning fork is attached to a 0.50m thin wire, causing a standing wave pattern, as shown. What is the speed of the waves on the string fund freq: ½λ = L f = 230Hz 3. A banjo has a string length of 80 cm. If v = 343 m/s, what is the frequency of the second harmonic? 1½ λ fits L λ = 2/3 L λ = 2/3(0.8m) λ = 0.53m

121 Ch11 HW#3 1 – 5 1. A mandolin string is 105 cm long. If it’s a cold day, the speed of sound is 335 m/s, what is the lowest possible frequency the string can hold? fund freq: ½λ = L ½λ = 1.05m λ = 2.10m 2. A 230 Hz tuning fork is attached to a 0.50m thin wire, causing a standing wave pattern, as shown. What is the speed of the waves on the string fund freq: ½λ = L f = 230Hz 3. A banjo has a string length of 80 cm. If v = 343 m/s, what is the frequency of the second harmonic? 1½ λ fits L λ = 2/3 L λ = 2/3(0.8m) λ = 0.53m

122 1. A mandolin string is 105 cm long. If it’s a cold day, the speed of sound is 335 m/s, what is the lowest possible frequency the string can hold? fund freq: ½λ = L ½λ = 1.05m λ = 2.10m 2. A 230 Hz tuning fork is attached to a 0.50m thin wire, causing a standing wave pattern, as shown. What is the speed of the waves on the string fund freq: ½λ = L f = 230Hz 3. A banjo has a string length of 80 cm. If v = 343 m/s, what is the frequency of the second harmonic? 1½ λ fits L λ = 2/3 L λ = 2/3(0.8m) λ = 0.53m

123 1. A mandolin string is 105 cm long. If it’s a cold day, the speed of sound is 335 m/s, what is the lowest possible frequency the string can hold? fund freq: ½λ = L ½λ = 1.05m λ = 2.10m 2. A 230 Hz tuning fork is attached to a 0.50m thin wire, causing a standing wave pattern, as shown. What is the speed of the waves on the string fund freq: ½λ = L f = 230Hz 3. A banjo has a string length of 80 cm. If v = 343 m/s, what is the frequency of the second harmonic? 1½ λ fits L λ = 2/3 L λ = 2/3(0.8m) λ = 0.53m

124 4. A banjo has a string length of 80 cm. If v = 343 m/s, what is the frequency of the 5 th harmonic? 5 th harmonic: 3λ = L λ = 0.27m 5. A 512 Hz “C” note tuning fork is attached to a 1.00m thin metal wire and set into a vibration, causing a standing wave pattern as shown. What is the speed of the waves on the wire? freq: 512Hz 2λ = L λ = 0.50m

125 4. A banjo has a string length of 80 cm. If v = 343 m/s, what is the frequency of the 5 th harmonic? 5 th harmonic: 3λ = L λ = 0.27m 5. A 512 Hz “C” note tuning fork is attached to a 1.00m thin metal wire and set into a vibration, causing a standing wave pattern as shown. What is the speed of the waves on the wire? freq: 512Hz 2λ = L λ = 0.50m

126 4. A banjo has a string length of 80 cm. If v = 343 m/s, what is the frequency of the 5 th harmonic? 5 th harmonic: 3λ = L λ = 0.27m 5. A 512 Hz “C” note tuning fork is attached to a 1.00m thin metal wire and set into a vibration, causing a standing wave pattern as shown. What is the speed of the waves on the wire? freq: 512Hz 2λ = L λ = 0.50m

127 Ch11.4 – Standing Waves in Air Columns Open at both ends: Fund freq: 1 st harmonic: Closed at both ends: Fund freq: 1 st harmonic: Combo (like lab):Fund freq:

128 Open at both ends: Antinodes at both ends Fund freq: 1 st harmonic: ½λ fits L λ fits L λ = 2L λ = L Closed at both ends: Fund freq: 1 st harmonic: Combo (like lab):Fund freq:

129 Open at both ends: Antinodes at both ends Fund freq: 1 st harmonic: ½λ fits L λ fits L λ = 2L λ = L Closed at both ends: Fund freq: 1 st harmonic: ½λ fits L λ fits L λ = 2L λ = L Combo (like lab):Fund freq:

130 Open at both ends: Antinodes at both ends Fund freq: 1 st harmonic: ½λ fits L λ fits L λ = 2L λ = L Closed at both ends: Fund freq: 1 st harmonic: ½λ fits L λ fits L λ = 2L λ = L Combo (like lab): Fund freq: ¼λ fits L λ = 4L

131 Ex1) What is the fundamental frequency of a 24cm tube ½-filled with water? What is the 1 st harmonic?

132 Ex1) What is the fundamental frequency of a 24cm tube ½-filled with water? What is the 1 st harmonic? fund freq 1 st harmonic ¼λ fits L 3/4λ fits L λ = 4L λ = 4/3L λ = 4(.12m) λ = 4/3(.12m) λ =.48m λ =.16m

133 Ex2) A native blows across the top of a 20cm piece of bamboo open at both ends. What is the fundamental frequency and the frequency of the 3 rd harmonic? fund 1 st 2 nd 3 rd

134 Ex2) A native blows across the top of a 20cm piece of bamboo open at both ends. What is the fundamental frequency and the frequency of the 3 rd harmonic? fund 1 st 2 nd 3 rd ½λ fits L 2λ fits L λ = 2L λ = ½L λ =.40m λ =.10m Ch11 HW#4 p431 68,69,80,104,105, 106, Bonus

135 Lab11.1 – Waves and Sound - due tomorrow - Ch11 HW#3 beginning of period

136 Ch11 HW#4 p431 68,69,80,104,105,106,108, + 2 Bonus 68. At what temp will the speed of sound at standard pressure equal 320 m / s ? 69. If a tuning fork puts out a freq of 440Hz, what is wavelength at 25°C? 104. A thin wire is stretched between 2 posts 50cm apart. It is bowed and set into oscillation. What are the wavelengths of the fund and 1 st overtone? 105. A taut string is fixed at both ends which are.50m apart. It is then set into resonance at its 6 th harmonic. What is the wavelength of 6 th ?

137 Ch11 HW#4 p431 68,69,80,104,105,106, Bonus 68. At what temp will the speed of sound at standard pressure equal 320 m / s ? v = v 0 + (.6)T 320 m / s = (.6)T T = -18°C 69. If a tuning fork puts out a freq of 440Hz, what is wavelength at 25°C? 104. A thin wire is stretched between 2 posts 50cm apart. It is bowed and set into oscillation. What are the wavelengths of the fund and 1 st overtone? 105. A taut string is fixed at both ends which are.50m apart. It is then set into resonance at its 6 th harmonic. What is the wavelength of 6 th ?

138 Ch11 HW#4 p431 68,69,80,104,105,106, Bonus 68. At what temp will the speed of sound at standard pressure equal 320 m / s ? v = v 0 + (.6)T 320 m / s = (.6)T T = -18°C 69. If a tuning fork puts out a freq of 440Hz, what is wavelength at 25°C? f = 440Hz λ = ? v = (.6)(25°C)=346 m / s 104. A thin wire is stretched between 2 posts 50cm apart. It is bowed and set into oscillation. What are the wavelengths of the fund and 1 st overtone?

139 Ch11 HW#4 p431 68,69,80,104,105,106, Bonus 68. At what temp will the speed of sound at standard pressure equal 320 m / s ? v = v 0 + (.6)T 320 m / s = (.6)T T = -18°C 69. If a tuning fork puts out a freq of 440Hz, what is wavelength at 25°C? f = 440Hz λ = ? v = (.6)(25°C)=346 m / s 104. A thin wire is stretched between 2 posts 50cm apart. It is bowed and set into oscillation. What are the wavelengths of the fund and 1 st overtone? Fund Freq: 1 st harmonic: ½λ fits L 1λ fits L λ = 2L λ = L λ = 1.0m λ = 0.50m

140 105. A taut string is fixed at both ends which are.50m apart. It is then set into resonance at its 6 th harmonic. What is the wavelength of 6 th ? Fundamental frequency:Add footballs, 6 th has 7 footballs: 106. A string is stretched between fixed posts 250cm apart and oscillates at its fundamental mode of 100Hz. What is the speed of the wave on the string? 108. A narrow tube 1.00m long is closed rigidly at both ends. If the speed of sound is 335 m / s, what is the freq of the fund osc mode?

141 105. A taut string is fixed at both ends which are.50m apart. It is then set into resonance at its 6 th harmonic. What is the wavelength of 6 th ? Fundamental frequency:Add footballs, 6 th has 7 footballs: 7 footballs = 3.5 waves 0.50m/3.5waves = 0.14m/wave 106. A string is stretched between fixed posts 250cm apart and oscillates at its fundamental mode of 100Hz. What is the speed of the wave on the string? 108. A narrow tube 1.00m long is closed rigidly at both ends. If the speed of sound is 335 m / s, what is the freq of the fund osc mode?

142 105. A taut string is fixed at both ends which are.50m apart. It is then set into resonance at its 6 th harmonic. What is the wavelength of 6 th ? Fundamental frequency:Add footballs, 6 th has 7 footballs: 7 footballs = 3.5 waves 0.50m/3.5waves = 0.14m/wave 106. A string is stretched between fixed posts 250cm apart and oscillates at its fundamental mode of 100Hz. What is the speed of the wave on the string? ½λ fits L λ = 2Lv = λ. f λ = 5.0m = (5.0m)(100s -1 ) = 500 m / s 108. A narrow tube 1.00m long is closed rigidly at both ends. If the speed of sound is 335 m / s, what is the freq of the fund osc mode?

143 108. A narrow tube 1.00m long is closed rigidly at both ends. If the speed of sound is 335 m / s, what is the freq of the fund osc mode? v = 335 m / s λ = 2m Bonus #1) A 25cm iron pipe is normally used for holding a flag, is open at both ends, and is attached to the side of a building. The wind is blowing, and a sound is produced. A nerdy physics student identifies the sound to be a frequency around 680Hz. What is the speed of sound there? ½λ fits L λ = 2Lv = λ. f λ = 0.50m =

144 108. A narrow tube 1.00m long is closed rigidly at both ends. If the speed of sound is 335 m / s, what is the freq of the fund osc mode? v = 335 m / s λ = 2m Bonus #1) A 25cm iron pipe is normally used for holding a flag, is open at both ends, and is attached to the side of a building. The wind is blowing, and a sound is produced. A nerdy physics student identifies the sound to be a frequency around 680Hz. What is the speed of sound there? ½λ fits L λ = 2Lv = λ. f λ = 0.50m = (0.50m)(680s -1 ) = 340 m / s

145 Bonus #2) What is the fundamental frequency of a 10cm tube closed at the bottom? What is the 9 th harmonic? ¼λ fits L λ = 4L λ = 0.40m 4.5λ fits L λ = 0.02m

146 Bonus #2) What is the fundamental frequency of a 10cm tube closed at the bottom? What is the 9 th harmonic? ¼λ fits L λ = 4L λ = 0.40m 4.5λ fits L λ = 0.02m

147 Ch28 – Quantum Theory Blackbody Radiation - all objects at different temps than their surroundings either give off or absorb thermal energy. Photoelectric effect - (Einstein’s Nobel Prize) Classic theory: Light is an E/M wave. So even low energy light, with high intensity should liberate electrons from “special” surface. Red light didn’t liberate any electrons. ‘special metal surface’

148 Photoelectric effect - (Einstein’s Nobel Prize) Classic theory: Light is an E/M wave. So even low energy light, with high intensity should liberate electrons from “special” surface. Red light didn’t liberate any electrons. Low intensity blue, however, could. e -1

149 Photoelectric effect - (Einstein’s Nobel Prize) Classic theory: Light is an E/M wave. So even low energy light, with high intensity should liberate electrons from “special” surface. Red light didn’t liberate any electrons. Low intensity blue, however, could. Violet also liberated electrons and gave a little KE to them. e -1

150 Photoelectric effect - (Einstein’s Nobel Prize) Classic theory: Light is an E/M wave. So even low energy light, with high intensity should liberate electrons from “special” surface. Red light didn’t liberate any electrons. Low intensity blue, however, could. Violet also liberated electrons and gave a little KE to them. Einstein explained: “Energy is quantized.” Comes in the form of photons - little bundles of energy. Red photons  low energy photons. Blue photons  higher energy photons. (Higher frequency = Higher energy) e -1 E = h. f e -1

151 Ex1) What is the energy of 500 nm light in Joules and electron-volts?

152 Bohr Model of the Atom: Electrons only exist at certain, stable orbits around the nucleus. - seek max stability in a base state - absorb photons and make quantum jumps to excited states - will make drops to get back to base state  give off photons on each drop - absorbed and emitted photons have energy (E = hf) or (E = hc/λ) If more energy is given to the electron than its ionization energy, the electron will leave the atom with some kinetic energy KE = hf – Φ the KE Energy of Work function of the electron photon hitting (the amt of energy as it leaves the electron required to ionize the atom) the atom

153 Ex) It takes 13.6 eV to ionize the electron from a hydrogen atom. If a photon of 80 nm is absorbed by the electron, will it ionize? If so how much KE? IE e -1 nucleus Ch28 HW#1

154 1. A monatomic gas is illuminated with visible light of wavelength 400nm. The gas is observed to absorb a photon of this light, bringing an electron in an atom to an excited state. a. If the initial state of the atom has an energy of -5.0eV, what is the energy of the state to which the atom was excited by the 400nm light? b. If the electron emits 600nm photon of light, what is the new energy state of the electron? c. At what other wavelength(s) outside the visible range do these atoms emit radiation after they are excited by the 400nm light? d. In the box, complete the energy level diagram that would be consistent with these observations. 0eV Ionized Atom -5eV e -1 Initial State nucleus

155 1. A monatomic gas is illuminated with visible light of wavelength 400nm. The gas is observed to absorb a photon of this light, bringing an electron in an atom to an excited state. a. If the initial state of the atom has an energy of -5.0eV, what is the energy of the state to which the atom was excited by the 400nm light? b. If the electron emits 600nm photon of light, what is the new energy state of the electron? c. At what other wavelength(s) outside the visible range do these atoms emit radiation after they are excited by the 400nm light? d. In the box, complete the energy level diagram that would be consistent with these observations. -1.9eV 0eV Ionized Atom -5eV e -1 Initial State nucleus

156 1. A monatomic gas is illuminated with visible light of wavelength 400nm. The gas is observed to absorb a photon of this light, bringing an electron in an atom to an excited state. a. If the initial state of the atom has an energy of -5.0eV, what is the energy of the state to which the atom was excited by the 400nm light? b. If the electron emits 600nm photon of light, what is the new energy state of the electron? c. At what other wavelength(s) outside the visible range do these atoms emit radiation after they are excited by the 400nm light? d. In the box, complete the energy level diagram that would be consistent with these observations. -1.9eV -4.0eV 0eV Ionized Atom -5eV e -1 Initial State nucleus

157 1. A monatomic gas is illuminated with visible light of wavelength 400nm. The gas is observed to absorb a photon of this light, bringing an electron in an atom to an excited state. a. If the initial state of the atom has an energy of -5.0eV, what is the energy of the state to which the atom was excited by the 400nm light? b. If the electron emits 600nm photon of light, what is the new energy state of the electron? c. At what other wavelength(s) outside the visible range do these atoms emit radiation after they are excited by the 400nm light? d. In the box, complete the energy level diagram that would be consistent with these observations. -1.9eV -4.0eV 0eV Ionized Atom -5eV e -1 Initial State nucleus

158 Ch29 – Quantum Mechanics - by 1920’s proven that light acts as particle and a wave. E/M radiation’s “wave/particle duality” De Broglie thought this might be characteristic of all things If the photons of E/M radiation travel as transverse waves and exhibit particle behaviors, then matter in motion must exhibit wave behavior DeBroglie Wavelength: momentum Ex1) Calculate the wavelength of me (m = 70 kg) walking around at 1 m/s. Ex2) Calculate the wavelength of an electron traveling at half the speed of light. (r = 0.053nm)

159 Ex3) A photon of wavelength 250nm ejects an electron from a metal. The ejected electron has a deBroglie wavelength of 0.85nm. a) Calc the KE of the electron. b) Assuming the KE found in (a) is the mas KE that it could have, calc the work function of the metal. c) The incident photon was created when an atom underwent an electron transition. On the energy level diagram, the transition labeled X corresponds to a photon of wavelength 400nm. Indicate which transition could be the source of the original 250nm photon by circling the correct letter. X c d e a b Ch29 HW#1

160 Ex3) A photon of wavelength 250nm ejects an electron from a metal. The ejected electron has a deBroglie wavelength of 0.85nm. a) Calc the KE of the electron. b) Assuming the KE found in (a) is the max KE that it could have, calc the work function of the metal. Photon energy: KE = hf – Φ 2.09eV = 4.97eV – Φ Φ = 2.88eV c) The incident photon was created when an atom underwent an electron transition. On the energy level diagram, the transition labeled X corresponds to a photon of wavelength 400nm. Indicate which transition could be the source of the original 250nm photon by circling the correct letter. X c d e Photon ‘created’ means an electron dropped and released a photon. a b A 400nm photon has less energy than a 250nm photon, so the 250nm photon would require a larger drop (d) Ch29 HW#1

161 Ch29 HW#1 1. Calculate the wavelength of an electron traveling at 1 mm/s. 2. What is the momentum of a subatomic particle with a wavelength of 500 nm?

162 Ch29 HW#1 1. Calculate the wavelength of an electron traveling at 1 mm/s. 2. What is the momentum of a subatomic particle with a wavelength of 500 nm?

163 Ch29 HW#1 1. Calculate the wavelength of an electron traveling at 1 mm/s. 2. What is the momentum of a subatomic particle with a wavelength of 500 nm?

164 3. A monatomic gas is illuminated with violet light of 350nm. a) What amount of energy is associated with this photon? b) On the diagram, draw this transition. The electron now emits red light at 650nm. c) What amount of energy is associated with this photon? d) On the diagram, draw this transition. e) What other wavelength is emitted? f) On the diagram, draw this transition. g) What frequency photon would ionize this atom? a) 350nm: c) 650nm: e) 2 nd emitted photon has an energy of E = = 1.64eV g) E = hf IE 0eV Ionized Atom -4eV e -1 Initial State nucleus

165 3. A monatomic gas is illuminated with violet light of 350nm. a) What amount of energy is associated with this photon? b) On the diagram, draw this transition. The electron now emits red light at 650nm. c) What amount of energy is associated with this photon? d) On the diagram, draw this transition. e) What other wavelength is emitted? f) On the diagram, draw this transition. g) What frequency photon would ionize this atom? a) 350nm: c) 650nm: e) 2 nd emitted photon has an energy of E = = 1.64eV g) E = hf IE 0eV Ionized Atom -4eV e -1 Initial State nucleus

166 3. A monatomic gas is illuminated with violet light of 350nm. a) What amount of energy is associated with this photon? b) On the diagram, draw this transition. The electron now emits red light at 650nm. c) What amount of energy is associated with this photon? d) On the diagram, draw this transition. e) What other wavelength is emitted? f) On the diagram, draw this transition. g) What frequency photon would ionize this atom? a) 350nm: c) 650nm: e) 2 nd emitted photon has an energy of E = = 1.64eV g) E = hf IE 0eV Ionized Atom -4eV e -1 Initial State nucleus

167 3. A monatomic gas is illuminated with violet light of 350nm. a) What amount of energy is associated with this photon? b) On the diagram, draw this transition. The electron now emits red light at 650nm. c) What amount of energy is associated with this photon? d) On the diagram, draw this transition. e) What other wavelength is emitted? f) On the diagram, draw this transition. g) What frequency photon would ionize this atom? a) 350nm: c) 650nm: e) 2 nd emitted photon has an energy of E = = 1.64eV g) E = hf IE 0eV Ionized Atom -4eV e -1 Initial State nucleus

168 3. A monatomic gas is illuminated with violet light of 350nm. a) What amount of energy is associated with this photon? b) On the diagram, draw this transition. The electron now emits red light at 650nm. c) What amount of energy is associated with this photon? d) On the diagram, draw this transition. e) What other wavelength is emitted? f) On the diagram, draw this transition. g) What frequency photon would ionize this atom? a) 350nm: c) 650nm: e) 2 nd emitted photon has an energy of E = = 1.64eV g) E = hf IE 0eV Ionized Atom -4eV e -1 Initial State nucleus

169 Ch29.2 Quantum Rev 1. A free electron with negligible kinetic energy is captured by a stationary proton to form an excited state of the hydrogen atom. During this process a photon of energy E a is emitted, followed shortly by another photon of energy 8.5eV. No further protons are emitted. The ionization energy of hydrogen is 13.6 electron volts. a. Determine the wavelength of the 8.5 eV photon. b. Determine the following for the first photon emitted: i) The energy, E a, of the photon ii) The frequency that corresponds to this energy d. The atom is in its ground state, when a 15 eV photon interacts with it. All of the photon’s energy is transferred to the electron, freeing it from the atom. Determine the following: i) The kinetic energy of the ejected electron. ii) The de Broglie wavelength of the electron

170 1. A free electron with negligible kinetic energy is captured by a stationary proton to form an excited state of the hydrogen atom. During this process a photon of energy E a is emitted, followed shortly by another photon of energy 8.5eV. No further protons are emitted. The ionization energy of hydrogen is 13.6 electron volts. a. Determine the wavelength of the 8.5 eV photon. b. Determine the following for the first photon emitted: (5.1eV drop) i) The energy, E a, of the photon 13.6 – 8.5 = 5.1eV ii) The frequency that corresponds to this energy E = hff = 1.23x10 15 Hz d. The atom is in its ground state, when a 15 eV photon interacts with it. All of the photon’s energy is transferred to the electron, freeing it from the atom. Determine the following: (8.5eV drop) i) The kinetic energy of the ejected electron. ii) The de Broglie wavelength of the electron. KE = hf – Φ = 15eV – 13.6eV = 1.4eV = 2.24x J ½mv 2 =2.24x v=7x10 5 m/s Ch29 HW#

171 Ch29 HW#2 1. The allowed energy levels of a simple hypothetical atom are -6.0eV, -3.0eV, and -1.0eV a) Draw and label the energy level diagram. b) Calc the wavelengths associated with each possible transition between energy levels for the atom. c) The atom has its electron is in the ground state when another electron traveling with a speed of 1.3x10 6 m/s collides with it. If all of the 2 nd electron’s kinetic energy is transferred to the ground state electron, can it get excited to the 2 nd energy level? ___ yes ___ no ___ it cannot be determined with the info given Justify answer IE ___eV n=3 ___eV n=2 ___eV n=1 ___eV (Ground state)

172 b) Calc the wavelengths associated with each possible transition between energy levels for the atom. IE 0eV n=3 --1eV n=2 -3eV n=1 -6eV (Ground state)

173 c) The atom has its electron is in the ground state when another electron traveling with a speed of 1.3x10 6 m/s collides with it. If all of the 2 nd electron’s kinetic energy is transferred to the ground state electron, can it get excited to the 2 nd energy level? ___ yes ___ no ___ it cannot be determined with the info given Justify answer. KE of electron: IE 0eV n=3 --1eV n=2 -3eV n=1 -6eV (Ground state)

174 c) The atom has its electron is in the ground state when another electron traveling with a speed of 1.3x10 6 m/s collides with it. If all of the 2 nd electron’s kinetic energy is transferred to the ground state electron, can it get excited to the 2 nd energy level? _ X _ yes ___ no ___ it cannot be determined with the info given Justify answer. KE of electron:It has enough energy to clear -3eV d) If the electron was in the 2 nd energy level and decayed back to the ground state, it emits a photon. i. Calc the energy of the emitted photon in joules ii. what region of E/M spectrum? ___ radio___ x-rays___ visible light ___ it cannot be determined with the info given. IE 0eV n=3 --1eV n=2 -3eV n=1 -6eV (Ground state) 3eV = ________ J

175 c) The atom has its electron is in the ground state when another electron traveling with a speed of 1.3x10 6 m/s collides with it. If all of the 2 nd electron’s kinetic energy is transferred to the ground state electron, can it get excited to the 2 nd energy level? _ X _ yes ___ no ___ it cannot be determined with the info given Justify answer. KE of electron:It has enough energy to clear -3eV d) If the electron was in the 2 nd energy level and decayed back to the ground state, it emits a photon. i. Calc the energy of the emitted photon in joules ii. what region of E/M spectrum? ___ radio___ x-rays_X_ visible light ___ it cannot be determined with the info given. IE 0eV n=3 --1eV n=2 -3eV n=1 -6eV (Ground state) 3eV = 4.8x J = 413 nm

176 Ch10,11 Rev p374 2,71,87, p429 4,7,55 2. When an object weighing 200N is hung from a vertical spring, the spring stretches 10cm, Calc the spring’s elastic constant kg of potatoes are put on a scale that is displaced 2.5 cm as a result. If the scale is pushed down a little and allowed to oscillate, what is the freq? 87. How long must a simple pendulum be if it is to have a period of 10sec?

177 Ch10,11 Rev p374 2,71,87, p429 4,7,55 2. When an object weighing 200N is hung from a vertical spring, the spring stretches 10cm, Calc the spring’s elastic constant kg of potatoes are put on a scale that is displaced 2.5 cm as a result. If the scale is pushed down a little and allowed to oscillate, what is the freq? 87. How long must a simple pendulum be if it is to have a period of 10sec?

178 Ch10,11 Rev p374 2,71,87, p429 4,7,55 2. When an object weighing 200N is hung from a vertical spring, the spring stretches 10cm, Calc the spring’s elastic constant kg of potatoes are put on a scale that is displaced 2.5 cm as a result. If the scale is pushed down a little and allowed to oscillate, what is the freq? 87. How long must a simple pendulum be if it is to have a period of 10sec?

179 Ch10,11 Rev p374 2,71,87, p429 4,7,55 2. When an object weighing 200N is hung from a vertical spring, the spring stretches 10cm, Calc the spring’s elastic constant kg of potatoes are put on a scale that is displaced 2.5 cm as a result. If the scale is pushed down a little and allowed to oscillate, what is the freq? 87. How long must a simple pendulum be if it is to have a period of 10sec?

180 Ch11 – 4. A wave on a string travels a 10m length in 2.0s. A harmonic disturbance of wavelength 0.50m is then generated on the string. What is the frequency? 7. A harmonic wave has a profile described by: What are amplitude, wavelength, and freq, if wave speed is 2.0 m / s ? 55. A groove on a monophonic phonograph record wiggles laterally such that its amplitude and frequency correspond to the sound recorded. If at a given moment the needle is moving thru the groove at 0.50 m / s, what would be the wiggle wavelength for a 1.5kHz tone? How many waves fit on a 1m long needle?

181 Ch11 – 4. A wave on a string travels a 10m length in 2.0s. A harmonic disturbance of wavelength 0.50m is then generated on the string. What is the frequency? 7. A harmonic wave has a profile described by: What are amplitude, wavelength, and freq, if wave speed is 2.0 m / s ? 55. A groove on a monophonic phonograph record wiggles laterally such that its amplitude and frequency correspond to the sound recorded. If at a given moment the needle is moving thru the groove at 0.50 m / s, what would be the wiggle wavelength for a 1.5kHz tone? How many waves fit on a 1m long needle?

182 Ch11 – 4. A wave on a string travels a 10m length in 2.0s. A harmonic disturbance of wavelength 0.50m is then generated on the string. What is the frequency? 7. A harmonic wave has a profile described by: What are amplitude, wavelength, and freq, if wave speed is 2.0 m / s ? A = 1.2cm λ = 10cm 55. A groove on a monophonic phonograph record wiggles laterally such that its amplitude and frequency correspond to the sound recorded. If at a given moment the needle is moving thru the groove at 0.50 m / s, what would be the wiggle wavelength for a 1.5kHz tone? How many waves fit on a 1m long needle?

183 Ch11 – 4. A wave on a string travels a 10m length in 2.0s. A harmonic disturbance of wavelength 0.50m is then generated on the string. What is the frequency? 7. A harmonic wave has a profile described by: What are amplitude, wavelength, and freq, if wave speed is 2.0 m / s ? A = 1.2cm λ = 10cm 55. A groove on a monophonic phonograph record wiggles laterally such that its amplitude and frequency correspond to the sound recorded. If at a given moment the needle is moving thru the groove at 0.50 m / s, what would be the wiggle wavelength for a 1.5kHz tone? How many waves fit on a 1m long needle? v = 0.5 m / s f = 1500Hz

184 Bonus exs: 1. Describe the overlap: 2. Someone rubs their finger around the rim of a crystal glass shown, and the sound emitted is measured to have a frequency of 2340Hz. If the air temp is 30°C, what is the height of the water in the glass? 15cm

185 Bonus exs: 1. Describe the overlap: 2. Someone rubs their finger around the rim of a crystal glass shown, and the sound emitted is measured to have a frequency of 2340Hz. If the air temp is 30°C, what is the height of the water in the glass? v = v 0 + (.6)T v = (.6)(30°C) Lv = m / s 15cm ¼λ fits L ¼λ = L ¼(.149m) = L L = 0.037m Water = 15cm – 3.7cm = 11.3cm

186 Quantum Mechanics Review A monochromatic source emits a 2.5 milliWatt beam of light of wavelength 450nm. a) Calc the energy of a photon in the beam. b) Calc the number of photons emitted by the source in 5 minutes. The beam is incident on the surface of a metal in a photo-electric experiment. The work function (IE) of this metal is 1.38x J. c) Calc the max speed of the emitted electrons. d) Calc the de Broglie wavelength of the most energetic electrons.

187 A monchromatic source emits a 2.5 milliWatt beam of light of wavelength 450nm. a) calc the energy of a photon in the beam. b) Calc the number of photons emitted by the source in 5 minutes. The beam is incident on the surface of a metal in a photo-electric experiment. The work function (IE) of this metal is 1.38x J. c)Calc the max speed of the emitted electrons. d) Calc the de Broglie wavelength of the most energetic electrons. a) b)

188 A monochromatic source emits a 2.5 milliWatt beam of light of wavelength 450nm. a) calc the energy of a photon in the beam. b) Calc the number of photons emitted by the source in 5 minutes. The beam is incident on the surface of a metal in a photo-electric experiment. The work function (IE) of this metal is 1.38x J. c)Calc the max speed of the emitted electrons. d) Calc the de Broglie wavelength of the most energetic electrons. a) b)

189 A monochromatic source emits a 2.5 milliWatt beam of light of wavelength 450nm. a) Calc the energy of a photon in the beam. b) Calc the number of photons emitted by the source in 5 minutes. The beam is incident on the surface of a metal in a photo-electric experiment. The work function (IE) of this metal is 1.38x J. c) Calc the max speed of the emitted electrons. d) Calc the de Broglie wavelength of the most energetic electrons. a) b) c)

190 A monochromatic source emits a 2.5 milliWatt beam of light of wavelength 450nm. a) Calc the energy of a photon in the beam. b) Calc the number of photons emitted by the source in 5 minutes. The beam is incident on the surface of a metal in a photo-electric experiment. The work function (IE) of this metal is 1.38x J. c) Calc the max speed of the emitted electrons. d) Calc the de Broglie wavelength of the most energetic electrons. a) b) c) d)

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197 3. To demonstrate standing waves, one end of a string is attached to a tuning fork with frequency 120 Hz. The other end of the string passes over a pulley and is connected to a suspended mass M as shown in the figure above. The value of M is such that the standing wave pattern has four “loops.” The length of the string from the tuning fork to the point where the string touches the top of the pulley is 1.20 m. The linear density of the string is ^ -4 kg/m, and remains constant throughout the experiment. (a) Determine the wavelength of the standing wave. (b) Determine the speed of transverse waves along the string. (c) The speed of waves along the string increases with increasing tension in the string. Indicate whether the value of M should be increased or decreased in order to double the number of loops in the standing wave pattern. Justify your answer. (d) If a point on the string at an antinode moves a total vertical distance of 4 cm during one complete cycle, what is the amplitude of the standing wave?


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