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Warm-Up: January 26, 2015 A 24.0 kg mass is attached to the bottom of a vertical spring, causing it to stretch 15.0 cm. What is the spring constant? What is the final potential energy stored in the spring?

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**First Semester Grading Scale**

65-75: B 55-65: C 45-55: D 0-45: F

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Lab Tomorrow You must wear closed-toe shoes.

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**Oscillatory Motion and Waves**

OpenStax Chapter 16

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Hooke’s Law Revisited When an elastic object is deformed, it experiences a restoring force. Elastic means that it is capable of returning to its original shape/size. Includes springs, plastic rulers, rubber bands, guitar strings, etc. The restoring force is given by Hooke’s Law

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Force Constant The force constant, k, is related to the rigidity (or stiffness) of a system. Larger k greater restoring force stiffer system Measured in N/m The slope of a Force vs. Displacement graph (if the graph is linear)

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You-Try 16.1 What is the force constant for the suspension system of a car that settles 1.20 cm when an 80.0 kg person gets in?

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You-Try 16.1 What is the force constant for the suspension system of a car that settles 1.20 cm when an 80.0 kg person gets in? 6.53x104 N/m

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**Energy in Hooke’s Law Work must be done in any deformation.**

Assuming no energy is lost to heat, sound, etc., then all work is transferred to potential energy. Since the force increases linearly with displacement, we can easily calculate the potential energy.

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**Work Potential Energy**

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You-Try 16.2 How much energy is stored in the spring of a tranquilizer gun that has a force constant of 50.0 N/m and is compressed m? If you neglect friction and the mass of the spring, at what speed will a 2.00 g projectile be ejected from the gun? 0.563 J 23.7 m/s

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Assignment Read Section 16.1 of OpenStax textbook (online): pages

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Warm-Up: January 27, 2015 A force of 20.0 N is applied to the tip of a ruler, causing it to deflect 4.00 cm. What is the force constant of the ruler?

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**Today’s Lab You will be assigned to a group.**

Your group’s goal is to determine the relationship between the following: The mass at the end of the string The length of the string The period of an oscillation (the time it takes to complete one oscillation). The angle of oscillation Materials allowed: String (and scissors to cut the string) Masses Rulers/Metersticks/Protractor Stopwatch (cell phone) Be sure to record everything in your lab notebook!

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**Lab Groups Group 1 Uriostegui Parra, Karla Peek, Angela Sutton, Foster**

Hy, Kevin Galac, Roger Regge Jezycki, Jocelyn Group 3 Moreno, Mark To, Frank Cdebaca, Paul Group 4 Gorman, Courtney Nguyen, Christina Dolphin, Jeremy Group 5 Lee, Justin Nguyen, Peter Lenhoff, Shane Group 6 Kibret, Elroi Basinger, Shelby Nava Saucedo, Hector Group 7 Le, Tiffany Garcia-Ayala, Diana Kirk, John Group 8 Randazzo, Joseph Wu, Tong Lenhoff, Erin Group 9 Lopez, Isabel Nguyen, Phat

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**Lab Reports Must Include**

Group member names Descriptive lab name Materials used Procedures followed Data obtained Calculations made Conclusions reached Summary

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Warm-Up: January 28, 2015 A g mass is attached to a rubber band, causing it to stretch 5.00 cm. How much potential energy is stored in the rubber band?

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**Period and Frequency in Oscillations**

OpenStax section 16.2 AP Physics 1

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Periodic Motion Periodic motion is motion that repeats itself at regular time intervals. Examples: Vibrating guitar string Pendulum Mass bobbing at the end of a spring

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Period and Frequency The period, T, is the time to complete one oscillation. Measured in seconds The frequency, f, is the number of oscillations per unit time. Measured in Hertz

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Example 16.3 A medical imaging device produces ultrasound by oscillating with a period of μs. What is the frequency of this oscillation? 2.50x106 Hz

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You-Try 16.3 The frequency of middle C on a typical musical instrument is 264 Hz. What is the time for one complete oscillation? 3.79 ms

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Think-Pair-Share Identify an event in your life (such as receiving a paycheck) that occurs regularly. Identify both the period and frequency of this event.

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Lab You have the remainder of class to work on your lab report with your lab group.

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Warm-Up: January 29, 2015 A stroboscope is set to flash every 8.00x10-5 s. What is the frequency of the flashes?

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**Simple Harmonic Motion: A Special Periodic Motion**

OpenStax section 16.3 AP Physics 1

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**Simple Harmonic Motion**

Simple harmonic motion is oscillatory motion for a system where the net force can be described by Hooke’s Law. Pendulums are sometimes considered simple harmonic motion – only for small angles. Equal/symmetric displacement on either side of the equilibrium position. The maximum displacement from equilibrium is called the amplitude.

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**Simple Harmonic Motion Example**

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Importance of SHM Period and frequency are independent of amplitude, so simple harmonic oscillators can be used as clocks. They are a good analogue for waves, including invisible ones (sound, electromagnetic)

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**Period and Frequency For simple harmonic oscillators:**

What do period and frequency not depend on?

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You-Try 16.4 If the shock absorbers in a car go bad, then the car will oscillate at the least provocation, such as when going over bumps in the road and after stopping. Calculate the frequency and period of these oscillations for such a car if the car’s mass (including its load) is 900. kg and the force constant of the suspension system is 6.53x104 N/m f=1.36 Hz T=0.738 s

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**Simple Harmonic Motion and Waves**

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**Simple Harmonic Motion and Waves**

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Example

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Think-Pair-Share Suppose you pluck a banjo string. You hear a single note that starts out loud and slowly quiets over time. Describe what happens to the period, frequency, and amplitude of the sound waves as the volume decreases.

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You-Try #18 A diver on a diving board is undergoing simple harmonic motion. Her mass is 55.0 kg and the period of her motion is s. The next diver is a male whose period of simple harmonic motion is 1.05 s. What is his mass if the mass of the board is negligible?

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**Assignments Read OpenStax Chapter 16 (through 16.3)**

OpenStax page 588 #1-7 OpenStax page 590 #1-21 odd

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Warm-Up: January 30, 2015 If the spring constant of a simple harmonic oscillator is doubled, by what factor will the mass of the system need to change in order for the frequency of the motion to remain the same?

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Lab Reports Due One person from each group collect lab notebooks from all group members and turn them in.

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Homework Questions?

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**OpenStax section 16.4 AP Physics 1**

The Simple Pendulum OpenStax section 16.4 AP Physics 1

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**The Simple Pendulum Small-diameter mass, called the pendulum bob**

String has negligible mass, but strong enough to not stretch appreciably Undergoes simple harmonic motion if θ<15°

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Simple Pendulum

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**Period of Simple Pendulum**

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**Period of Simple Pendulum**

Does not depend on mass. Does not depend on amplitude (for θ<15°) Can be finely adjusted, and can make excellent clocks. Can also be used to solve for g.

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You-Try 16.5 What is the acceleration due to gravity in a region where a simple pendulum having a length of cm has a period of s?

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Think-Pair-Share What is the effect on the period of a pendulum if you double its length?

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You-Try 22 What is the length of a pendulum that has a period of s? Let g=9.80 m/s2.

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You-Try 26 The pendulum on a cuckoo clock is 5.00 cm long. What is its frequency? Let g=9.80 m/s2.

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**Assignments Read OpenStax Chapter 16 (through 16.4)**

OpenStax page 588 #1-8 OpenStax page 590 #1-33 odd

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Warm-Up: February 2, 2015 Punxsutawney Phil, seer of seers, prognosticator of prognosticators, has an extremely accurate pendulum clock in his secret lair. The period of this clock is exactly six weeks. What is the length of this pendulum clock? Is your answer realistic? Why or why not?

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**American Mathematics Competition**

New date and time Wednesday, February 25 Time TBD

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Homework Questions?

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**Energy and the Simple Harmonic Oscillator**

OpenStax Section 16.5 AP Physics 1

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**Simple Harmonic Oscillators**

Energy is conserved Maximum speed occurs at equilibrium position.

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**Pendulums (small θ) Energy is conserved**

Maximum speed occurs at equilibrium position.

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You-Try 16.6 Suppose that a car is 900. kg and has a suspension system that has a force constant of kN/m. The car hits a bump and bounces with an amplitude of m. What is its maximum velocity (assuming no damping)? 0.852 m/s

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You-Try 36 Near the top of the Citigroup Center building in New York City, there is an object with mass of 4.00x105 kg on springs that have adjustable force constants. Its function is to dampen wind-driven oscillations of the building by oscillating at the same frequency as the building is being driven; the driving force is transferred to the object, which oscillates instead of the entire building. What effective force constant should the springs have to make the object oscillate with a period of s? What energy is stored in the springs for a 2.00 m displacement from equilibrium?

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**Uniform Circular Motion and Simple Harmonic Motion**

OpenStax section 16.6 AP Physics 1

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**Circular Motion Simple Harmonic Motion**

An object moving in uniform circular motion can be used as an analogue for simple harmonic motion.

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The Equations

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You-Try 40 A ladybug sits 12.0 cm from the center of a Beatles album spinning at 33.3 rpm. What is the maximum velocity of its shadow on the wall behind the turntable, if illuminated parallel to the record by the parallel rays of the setting sun? 0.419 m/s

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**Assignments Read OpenStax Chapter 16 (through 16.6)**

OpenStax page 588 #1-9 OpenStax page 590 #1-39 odd

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Warm-Up: February 3, 2015 The device pictured entertains infants while keeping them from wandering. The child bounces in a harness suspended from a door frame by a spring. If the spring stretches m while supporting an 8.00 kg child, what is its spring constant? What is the time for one complete bounce? What is the child’s maximum velocity if the amplitude of her bounce is m?

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Homework Questions?

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**Damped Harmonic Motion**

OpenStax Section 16.7 AP Physics 1

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**Friction is Real! Friction is not always negligible.**

Damping is the slowing and stopping of oscillations, caused by a non-conservative force (such as friction). Damping is sometimes part of a design (such as a car’s shock absorbers). For small damping, the amplitude slowly decreases while period and frequency are nearly unchanged.

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Damping Non-conservative work removes mechanical energy (usually to thermal energy).

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Large Damping Large damping causes the period to increase and the frequency to decrease. Very large damping prevents oscillation – the system just returns to equilibrium. Critical damping is the amount of damping that returns a system to equilibrium as quickly as possible. Overdamped systems return to equilibrium slower than critical damping.

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Think-Pair-Share Which is critical damping? Which is overdamping?

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**Applications of Critical Damping**

Car shock absorbers Bathroom scale

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You-Try 16.7 Suppose a kg object is connected to a spring as shown, but there is simple friction between the object and the surface, and the coefficient of kinetic friction is equal to The force constant of the spring is 50.0 N/m. Use g=9.80 m/s2. What is the frictional force between the surfaces? What total distance does the object travel if it is released from rest m from equilibrium?

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Warm-Up: February 4, 2015 A novelty clock has a kg mass object bouncing on a spring that has a force constant of 1.25 N/m. What is the maximum velocity of the object if the object bounces 3.00 cm above and below the equilibrium position? How many Joules of kinetic energy does the object have at its maximum velocity?

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Homework Questions?

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**Forced Oscillations and Resonance**

OpenStax section 16.8 AP Physics 1

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Think-Pair-Share What do you have to do to swing high on a swing?

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Natural Frequency The natural frequency is the frequency at which it would oscillate if there were no driving and no damping force. If you drive a system at a frequency equal to its natural frequency, its amplitude will increase. This is called resonance. A system being driven at its natural frequency is said to resonate.

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**Resonance The highest amplitude oscillations occur when:**

The system is driven at its natural frequency There is minimal damping

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Think-Pair-Share A famous trick involves a performer singing a note toward a crystal glass until the glass shatters. Explain why the trick works in terms of resonance and natural frequency.

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Tacoma Narrows Bridge

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You-Try 46 A suspension bridge oscillates with an effective force constant of 1.00x108 N/m. How much energy is needed to make it oscillate with an amplitude of m? If soldiers march across the bridge with a cadence equal to the bridge’s natural frequency and impart 1.00x104 J of energy each second, how long does it take for the bridge’s oscillations to go from m to m amplitude?

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**Assignments Read OpenStax Chapter 16 (through 16.8)**

OpenStax page 588 #1-13 OpenStax page 590 #1-45 odd

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Warm-Up: February 5, 2015 How much energy must the shock absorbers of a 1200 kg car dissipate in order to damp a bounce that initially has a velocity of m/s at the equilibrium position? Assume the car returns to its original vertical position.

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Homework Questions?

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Mock AP Test Tentatively scheduled for April 18

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AMC Wednesday, February 25 4th period and lunch

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**OpenStax section 16.9 AP Physics 1**

Waves OpenStax section 16.9 AP Physics 1

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Waves A wave is a disturbance that propagates, or moves from the place it was created. Waves carry energy, not matter. Similar to simple harmonic motion, waves have a period, frequency, and amplitude. Waves also have a wave velocity, the velocity at which the disturbance moves. Waves also have a wavelength, λ, the distance between identical parts of the wave.

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Example Wave

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Wave Speed

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You-Try 16.8 Calculate the wave velocity of an ocean wave if the distance between wave crests is 10.0 m and the time for a sea gull to bob up and down is 5.00 s. 2.00 m/s

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**Transverse vs. Longitudinal**

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**Transverse vs. Longitudinal**

In transverse waves, also called shear waves, the direction of energy transfer and the direction of displacement are perpendicular. Examples: strings on musical instruments, light In longitudinal waves, also called compressional waves, the direction of energy transfer and the direction of displacement are parallel. Example: sound Some waves, such as ocean waves, are a combination of transverse and longitudinal.

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You-Try 52 What is the wavelength of the waves you create in a swimming pool if you splash your hand at a rate of 2.00 Hz and the waves propagate at m/s?

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**Superposition and Interference**

OpenStax section 16.10 AP Physics 1

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**Superposition Most real-world waves are combinations of simple waves.**

When two or more waves arrive at the same point, their disturbances are added together. This is called superposition. In constructive interference, crest meets crest, and trough meets trough, and the resultant is a wave with a larger amplitude. In destructive interference, crest meets trough, and resulting amplitude is smaller than either original amplitude. Amplitude is zero for pure destructive interference.

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**Pure Constructive Interference**

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**Pure Destructive Interference**

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PhET Waves on a String wave-on-a-string_en.jar

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Warm-Up: February 6, 2015 Radio waves transmitted through space at 3.00x108 m/s by the Voyager spacecraft have a wavelength of m. What is their frequency?

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More Superposition

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Standing Waves Sometimes waves superimpose in a way that causes an apparent lack of sideways motion. These waves are called standing waves. Standing waves have points that do not move, called nodes. The points that move the most are called antinodes.

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PhET Wave on a String Green dots are nodes

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**Fundamental Frequency**

The fundamental frequency is the lowest possible frequency for a standing wave. Overtones or harmonics are multiples of the fundamental frequency.

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Overtones

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Beats The superposition of two waves of similar frequency has a frequency that is the average of the two. This wave fluctuates in amplitude, or beats, in the beat frequency.

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You-Try 58 The middle-C hammer of a piano hits two strings, producing beats of 1.50 Hz. One of the strings is tuned to Hz. What frequencies could the other string have?

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You-Try 60 Twin jet engines on an airplane are producing an average sound frequency of Hz with a beat frequency of Hz. What are their individual frequencies?

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**Energy in Waves: Intensity**

OpenStax section 16.11 AP Physics 1

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**Wave Energy Wave energy is related to wave amplitude**

The intensity, I, of a wave is the power, P, carried through area A.

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**Intensity Valid for any flow of energy. Has units of W/m2.**

Other intensity units include decibels. 90 decibel = 10-3 W/m2

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You-Try 16.9 The average intensity of sunlight on Earth’s surface is about 700. W/m2. Calculate the amount of energy that falls on a solar collector having an area of m2 in 4.00 hours. What intensity would such sunlight have if concentrated by a magnifying glass onto an area 200. times smaller than its own?

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Warm-Up: February 9, 2015 If two identical waves, each having an intensity of 1.00 W/m2, interfere perfectly constructively, what is the intensity of the resulting wave?

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**Assignments Read OpenStax Chapter 16 OpenStax page 588 #1-18**

OpenStax page 590 #1-71 odd

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Homework Questions?

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Test Questions With your partner, write 3 multiple choice and/or multiple select questions. Indicate the correct answer(s). For computational questions, show work leading to the correct answer(s).

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Simple Harmonic Motion Repeated motion with a restoring force that is proportional to the displacement. A pendulum swings back and forth. pendulum A spring.

Simple Harmonic Motion Repeated motion with a restoring force that is proportional to the displacement. A pendulum swings back and forth. pendulum A spring.

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