1. Ch14.1 – Waves
Wave – rhythmic disturbance, carries energy through matter or space.
Transverse wave – wave vibrates perpendicular to the direction of travel
-like a rope.
Longitudinal wave (compression) – wave vibrates parallel to the motion
of the wave, like a slinky.

2. Formulas: v = λ ∙ f
f = 1/T
Freq units: Waves/sec (Hertz)
Period units: sec/wave
frequency
velocity
wavelength
Period (Time it takes for one wave to pass)
freq
(# of waves per second)

3. Wave – rhythmic disturbance, carries energy through matter or space.
Ch14.1 – Waves
Wave – rhythmic disturbance, carries energy through matter or space.
Transverse wave – wave vibrates perpendicular to the direction of travel
- like a rope.
Longitudinal wave (compression) – wave vibrates parallel to the motion of the wave, like a slinky.
Formulas: v = λ ∙ f
f = 1/T
Freq units: Waves/sec (Hertz)
Period units: sec/wave
Wavelength, (λ)
crest
Amplitude
trough
frequency
velocity
wavelength
Period (Time it takes for one wave to pass)
Freq
(# of waves
per second)

4. Ex1) A sound wave has a frequency of 262 Hz and a wavelength measured at 1.29 m.
a) What is the speed of the wave?
b) How long will it take the wave to travel the length of
a football field, 91.4m?
c) What is the period of the wave?
HW#1) A sound wave produced by a clock chime is heard 515 m away 1.50 s later.
a. What is the speed of sound of the clock’s chime in air?
b. The sound wave has a frequency of 436 Hz. What is its period?
c. What is its wavelength?

5. Ex1) A sound wave has a frequency of f = 262 Hz and a wavelength measured at λ = 1.29 m.
a) What is the speed of the wave?
b) How long will it take the wave to travel the length of a football field, 91.4m?
c) What is the period of the wave?
v=λ∙f
=(1.29m)(2621/sec)
=338m/s
d = v∙ t t = d/v = 91.4m/338m/s
= .27sec
T=? T=1/f = 1/262 1/sec = .004sec
HW#1) A sound wave produced by a clock chime is heard 515 m away 1.50 s later.
a. What is the speed of sound of the clock’s chime in air?
b. The sound wave has a frequency of 436 Hz. What is its period?
c. What is its wavelength?
(v = λ∙f) or (v = d/t)?
v = 515m/1.5sec
= 343m/s
T = ? T = 1/f = 1/436 1/sec = .002sec
v = λ∙ f
λ= v/f = 343m/s/436 1/sec = .8m

6. HW#7) A periodic longitudinal wave that has a frequency of 20
HW#7) A periodic longitudinal wave that has a frequency of 20.0 Hz travels along a coil spring. If the distance between successive compressions is .400 m, what is the speed of the wave?

7. HW#7) A periodic longitudinal wave that has a frequency of 20
HW#7) A periodic longitudinal wave that has a frequency of 20.0 Hz travels along a coil spring. If the distance between successive compressions is .400 m, what is the speed of the wave?
f = 20.0 Hz
v = λ ∙ f
= (.4m) (20 1/sec) = 8 m/s
λ = .4m
v =

8. CH14 HW #1 1–7
In class
A hiker shouts toward a vertical cliff 685 miles away. The echo is heard 4.00 sec later.
a. What is the speed of sound of the hiker’s voice in air?
b. The wavelength of the sound is .750 m. What is its frequency?
c. What is the period of the wave?
3. If you want to increase the wavelength of waves in a rope should you shake it at a higher or lower frequency?

9. (v = λ ∙ f) f = v/λ = 342.5m/s/.75m = 456.7 Hz
CH14 HW #1 1–7
In class
A hiker shouts toward a vertical cliff 685 miles away. The echo is heard 4.00 sec later.
a. What is the speed of sound of the hiker’s voice in air?
b. The wavelength of the sound is .750 m. What is its frequency?
c. What is the period of the wave?
3. If you want to increase the wavelength of waves in a rope should you shake it at a higher or lower frequency?
v = d/t = 685m/2s = 342.5m/s
(v = λ ∙ f) f = v/λ = 342.5m/s/.75m = Hz
T = 1/f = 1/456.7s-1 = .002s

10. (v = λ ∙ f) f = v/λ = 342.5m/s/.75m = 456.7 Hz
CH14 HW #1 1–7
In class
A hiker shouts toward a vertical cliff 685 miles away. The echo is heard 4.00 sec later.
a. What is the speed of sound of the hiker’s voice in air?
b. The wavelength of the sound is .750 m. What is its frequency?
c. What is the period of the wave?
3. If you want to increase the wavelength of waves in a rope should you shake it at a higher or lower frequency? Speed determined medium!
(v = λ ∙ f)
v = d/t = 685m/2s = 342.5m/s
(v = λ ∙ f) f = v/λ = 342.5m/s/.75m = Hz
T = 1/f = 1/456.7s-1 = .002s
Shake Fast :
(Higher frequency)
shorter wavelength
Shake slow
(Low freq)
Longer wavelength

11. f = 5 waves/.1 sec = 50 Hz λ = 1.2cm = .012m
4. What is the speed of a periodic wave disturbance that has a frequency of 2.50 Hz and a wavelength of .600 m?
5. The speed of a transverse wave in a string is 15.0 m/s. If a source produces a disturbance that has a frequency of 5.00 Hz, what is its wavelength?
6. Five pulses are generated every .100 s in a tank of water. What is the speed of propagation of the wave if the wavelength of the surface wave is 1.20 cm?
7. In class
f = 5 waves/.1 sec = 50 Hz
λ = 1.2cm = .012m

12. f = 5 waves/.1 sec = 50 Hz λ = 1.2cm = .012m
4. What is the speed of a periodic wave disturbance that has a frequency of 2.50 Hz and a wavelength of .600 m?
5. The speed of a transverse wave in a string is 15.0 m/s. If a source produces a disturbance that has a frequency of 5.00 Hz, what is its wavelength?
6. Five pulses are generated every .100 s in a tank of water. What is the speed of propagation of the wave if the wavelength of the surface wave is 1.20 cm?
7. In class
v = λ ∙ f = (.6m)(2.5s-1) = 1.5 m/s
f = 5 waves/.1 sec = 50 Hz
λ = 1.2cm = .012m

13. λ = v/f = 15.0m/s / 5.0s-1 = 3m f = 5 waves/.1 sec = 50 Hz
4. What is the speed of a periodic wave disturbance that has a frequency of 2.50 Hz and a wavelength of .600 m?
5. The speed of a transverse wave in a string is 15.0 m/s. If a source produces a disturbance that has a frequency of 5.00 Hz, what is its wavelength?
6. Five pulses are generated every .100 s in a tank of water. What is the speed of propagation of the wave if the wavelength of the surface wave is 1.20 cm?
7. In class
v = λ ∙ f = (.6m)(2.5s-1) = 1.5 m/s
λ = v/f = 15.0m/s / 5.0s-1 = 3m
f = 5 waves/.1 sec = 50 Hz
λ = 1.2cm = .012m

14. λ = v/f = 15.0m/s / 5.0s-1 = 3m 1/sec f = 5 waves/.1 sec = 50 Hz
4. What is the speed of a periodic wave disturbance that has a frequency of 2.50 Hz and a wavelength of .600 m?
5. The speed of a transverse wave in a string is 15.0 m/s. If a source produces a disturbance that has a frequency of 5.00 Hz, what is its wavelength?
6. Five pulses are generated every .100 s in a tank of water. What is the speed of propagation of the wave if the wavelength of the surface wave is 1.20 cm?
7. In class
v = λ ∙ f = (.6m)(2.5s-1) = 1.5 m/s
λ = v/f = 15.0m/s / 5.0s-1 = 3m
1/sec
f = 5 waves/.1 sec = 50 Hz
λ = 1.2cm = .012m
v = λ ∙ f
= (0.12m)(50s-1)
= .6m/s

15. Ch14.2 – Wave Behavior
Incident wave – wave going in
Reflected wave – wave going out.
Reflection at a fixed boundary:
Reflection at a moveable boundary:
Passing from dense to less dense medium:
Passing from less dense to more dense medium:

16. Ch14.2 – Wave Behavior
Incident wave – wave going in
Reflected wave – wave going out.
Reflection at a fixed boundary:
Reflection at a moveable boundary:
Passing from dense to less dense medium:
Passing from less dense to more dense medium:
Wave reflects 180o out of phase.
Crest comes back as a trough.
Wave reflects in phase.
Crest comes back as crest.
Part of wave continues upright,
part reflects off interface upright.
(Acts like moveable boundary.)
part reflects off interface as trough.
(Acts like fixed boundary.)

17. Superposition of Waves
Constructive interference – waves add energy
Ex1)
Ex2)
Destructive Interference – waves cancel energy
Ex3)
Ex4)
Ex5)

18. Superposition of Waves
Constructive interference – waves add energy
Ex1)
Ex2)
Destructive Interference – waves cancel energy
Ex3)
Ex4)
Ex5)
Ch14 HW#2 8 – 11

19. Lab14.1 – Waves
- due next day
- Ch14 HW#2 due at beginning of period

20. Ch14 HW#2 8-11
8. A wave is sent along a spring. The spring is attached to a moveable pivot, as shown. What does the reflection look like, upright or inverted?
9. A long spring runs across the floor of a room and out the door. A pulse is sent along the spring. After a few seconds, an inverted pulse returns. Is the spring attached to the wall in the next room or is it lying loose on the floor?
10. A pulse is sent along a thin rope that is attached to a thick rope, which is tied to a wall, as shown. At point A part of the wave transmits though to the thin rope and part reflects back into the thick rope. What does each part look like?

21. Ch14 HW#2 8-11
8. A wave is sent along a spring. The spring is attached to a moveable pivot, as shown. What does the reflection look like, upright or inverted?
Upright
9. A long spring runs across the floor of a room and out the door. A pulse is sent along the spring. After a few seconds, an inverted pulse returns. Is the spring attached to the wall in the next room or is it lying loose on the floor?
10. A pulse is sent along a thin rope that is attached to a thick rope, which is tied to a wall, as shown. At point A part of the wave transmits though to the thin rope and part reflects back into the thick rope. What does each part look like?

22. Ch14 HW#2 8-11
8. A wave is sent along a spring. The spring is attached to a moveable pivot, as shown. What does the reflection look like, upright or inverted?
Upright
9. A long spring runs across the floor of a room and out the door. A pulse is sent along the spring. After a few seconds, an inverted pulse returns. Is the spring attached to the wall in the next room or is it lying loose on the floor? Attached to wall
10. A pulse is sent along a thin rope that is attached to a thick rope, which is tied to a wall, as shown. At point A part of the wave transmits though to the thin rope and part reflects back into the thick rope. What does each part look like?

23. Ch14 HW#2 8-11
8. A wave is sent along a spring. The spring is attached to a moveable pivot, as shown. What does the reflection look like, upright or inverted?
Upright
9. A long spring runs across the floor of a room and out the door. A pulse is sent along the spring. After a few seconds, an inverted pulse returns. Is the spring attached to the wall in the next room or is it lying loose on the floor? Attached to wall
10. A pulse is sent along a thin rope that is attached to a thick rope, which is tied to a wall, as shown. At point A part of the wave transmits though to the thin rope and part reflects back into the thick rope. What does each part look like?

24. Sketch the resultant of each wave as the centers overlap on the dashed line:b) c)

25. Sketch the resultant of each wave as the centers overlap on the dashed line:b) c)

26. Ch15.1 – Sound Sound waves are longitudinal waves.
- cause small pressure changes that are detected by ear.
- transmit through solids and liquids the same way.
- slower through denser materials, but faster if material is elastic.
Speed of Sound Through Various Media
Air (0oC) m/s
*Air (20oC) m/s (HW#1)
Water (25oC) m/s
Sea Water(25oC) m/s
Iron (25oC) m/s
Rubber (25oC) m/s
Ex1) A tuning fork produces a sound wave in air with a frequency
of Hz. At a room temp the speed of sound is 343 m/s.
What is the wavelength?

27. Ch15.1 – Sound Sound waves are longitudinal waves.
- cause small pressure changes that are detected by ear.
- transmit through solids and liquids the same way.
- slower through denser materials, but faster if material is elastic.
Speed of Sound Through Various Media
Air (0oC) m/s
*Air (20oC) m/s (HW#1)
Water (25oC) m/s
Sea Water(25oC) m/s
Iron (25oC) m/s
Rubber (25oC) m/s
Ex1) A tuning fork produces a sound wave in air with a frequency
of Hz. At a room temp the speed of sound is 343 m/s.
What is the wavelength?
f = 261.6Hz
v = 343 m/s
λ = ?

28. Loudness – perception of sound intensity
Sound Level – measured in decibels
- measures the range from the faintest heard sound to the loudest
sounds.
- 10 dB increase is perceived jet engine – 110db
as being twice as loud. concert –
- 50,000 people yelling for 90 minutes
have the thermal energy ear damage – 70db
equivalent of a cup of coffee.
classroom –
this class –
faint sound – 0db
(threshold of hearing)
Pitch – related to frequency (High pitch = High Frequency)

29. Freq goes down. (v=λ.f) Ch15 HW#1
Doppler Effect – an apparent change in the pitch of a sound.
(High pitch as approaches, low pitch as recedes.)
Velocity of sound is a constant
(determined by the medium!)
Wavelengths get scrunched (small λ)
Frequency goes up (v=λ.f)
Wavelengths expand (big λ)
Freq goes down. (v=λ.f)
Ch15 HW#1

30. Lab15.1 Speed of Sound with Cymbals
- due tomorrow
- Ch15 HW#1 due at beginning of period

31. Ch15 HW#1 1 – 4
Find the frequency of a sound wave moving in air at room temperature with a wavelength of .667m.
f = ?
v = 343 m/s
λ = 0.667m
2. The human ear can detect sounds with frequencies between 20 Hz and 16,000 Hz. Find the largest and smallest wavelengths the ear can detect, assuming that the sound travels through air with a speed of 343 m/s.
f = 20Hz f = 16,000Hz
v = 343 m/s v = 343 m/s
λ = ? λ = ?

32. Ch15 HW#1 1 – 4
Find the frequency of a sound wave moving in air at room temperature with a wavelength of .667m.
f = ?
v = 343 m/s
λ = 0.667m
2. The human ear can detect sounds with frequencies between 20 Hz and 16,000 Hz. Find the largest and smallest wavelengths the ear can detect, assuming that the sound travels through air with a speed of 343 m/s.
f = 20Hz f = 16,000Hz
v = 343 m/s v = 343 m/s
λ = ? λ = ?

33. If you clap your hands and hear the echo from a distant wall 0
If you clap your hands and hear the echo from a distant wall 0.20 s later, how far away is the wall?
4. What is the frequency of sound in air having a wavelength equal to the diameter of a 15 in. (38 cm) sub woofer speaker?
Of a 3.0 in (7.6 cm) tweeter? Use 343 m/s for speed of sound.
f = ? f = ?
v = 343 m/s v = 343 m/s
λ = 0.38m λ = 0.076m

34. If you clap your hands and hear the echo from a distant wall 0
If you clap your hands and hear the echo from a distant wall 0.20 s later, how far away is the wall?
4. What is the frequency of sound in air having a wavelength equal to the diameter of a 15 in. (38 cm) sub woofer speaker?
Of a 3.0 in (7.6 cm) tweeter? Use 343 m/s for speed of sound.
f = ? f = ?
v = 343 m/s v = 343 m/s
λ = 0.38m λ = 0.076m
d = v.t = 343m/s sec =

35. Ch15.2 – Physics of Music Characteristic of 1 wavelength: crest trough
Characteristic of 1 standing wave:
reflection perfectly overlaps crest crest
constructive destructive
interference interference
(antinodes) (nodes)

36. Ch15.2 – Physics of Music
Standing waves on strings – caused by constructive/destructive interference patterns that end on a node.

37. Nodes L Fundamental frequency: ½λ fits L λ = 2L Anitnodes
1st harmonic:
1λ fits L
λ = L
Nodes
2nd harmonic:
1½ λ fits L
λ = 2/3L
String instruments have different lengths and thicknesses of strings
that can vibrate at different frequencies (diff pitches).

38. Ex1) A guitar string is 64 cm long
Ex1) A guitar string is 64 cm long. If the speed of sound is 343m/s, what is the lowest possible frequency the string can hold?
Ex2) A 256 Hz “C” note is played on a piano. If the speed of sound is 343m/s ,
what is the length of the string?
Ex3) A banjo has a string length of 80 cm. if v = 343m/s , what is the frequency
of the 1st harmonic?

39. Ex1) A guitar string is 64 cm long
Ex1) A guitar string is 64 cm long. If the speed of sound is 343m/s, what is the lowest possible frequency the string can hold?
fund freq:
½λ=L
½λ = 0.64m
λ = 1.28m
Ex2) A 256 Hz “C” note is played on a piano. If the speed of sound is 343m/s ,
what is the length of the string?
f = 256Hz
L = ½λ = 0.67m
Ex3) A banjo has a string length of 80 cm. if v = 343m/s , what is the frequency
of the 1st harmonic?
1st harmonic:
1λ fits L
λ = 0.80m
Ch15 HW#2 5 – 8

40. Ch15 HW#2 5 – 8 ½λ = L ½λ = 1.05m λ = 2.10m f = 512Hz λ = 2/3 L
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
A 512 Hz “C” note is played on a piano. If the speed of sound is 343 m/s,
what is the length of the string?
f = 512Hz
7. 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

41. Ch15 HW#2 5 – 8 ½λ = L ½λ = 1.05m λ = 2.10m f = 512Hz λ = 2/3 L
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
A 512 Hz “C” note is played on a piano. If the speed of sound is 343 m/s,
what is the length of the string?
f = 512Hz
½λ = L =
7. 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

42. Fund Freq 1st harmonic λ = L = 0.95m
8. A bass guitar has a string length of 95 cm. If v = 343 m/s, what is the frequency of the first harmonic?
Fund Freq
1st harmonic
λ = L = 0.95m

43. Fund Freq 1st harmonic λ = L = 0.95m
8. A bass guitar has a string length of 95 cm. If v = 343 m/s, what is the frequency of the first harmonic?
Fund Freq
1st harmonic
λ = L = 0.95m

44. Ch15.3 – Waves in Pipes Reminder: standing wave:
Closed Pipes – antinode at open end, node at closed end.
Fundamental Freq: 1st Harmonic:
Ch15.3 – Waves in Pipes
Ex1) A 512 Hz is held above a closed pipe 16 cm long when sound resonates. What is the speed of sound?

45. Ch15.3 – Waves in Pipes ¼ λ fits L ¾λ fits L λ = 4L λ = 4/3 L
Reminder: standing wave:
Closed Pipes – antinode at open end, node at closed end.
Fundamental Freq: 1st Harmonic:
¼ λ fits L ¾λ fits L
λ = 4L λ = 4/3 L
Ch15.3 – Waves in Pipes
Ex1) A 512 Hz tuning fork is held above a closed pipe 16 cm long when sound resonates. What is the speed of sound?

46. Ch15.3 – Waves in Pipes ¼ λ fits L ¾λ fits L λ = 4L λ = 4/3 L
Reminder: standing wave:
Closed Pipes – antinode at open end, node at closed end.
Fundamental Freq: 1st Harmonic:
¼ λ fits L ¾λ fits L
λ = 4L λ = 4/3 L
Ch15.3 – Waves in Pipes
Ex1) A 512 Hz tuning fork is held above a closed pipe 16 cm long when sound resonates. What is the speed of sound?
¼ λ fits L v = λ.f
λ = 4(.16m) = (0.64m)(512 s-1)
λ = 0.64m = 328 m/s

47. Spacings – resonance will occur again when the closed pipe is
Spacings – resonance will occur again when the closed pipe is lengthened every 1/2λ.
Ex2) A 392 Hz tuning fork resonates sound waves in closed pipes that
are 21 cm long and 63 cm. What is the speed of sound?

48. Spacings – resonance will occur again when the closed pipe is
Spacings – resonance will occur again when the closed pipe is lengthened every 1/2λ.
Ex2) A 392 Hz tuning fork resonates sound waves in closed pipes that
are 21 cm long and 63 cm. What is the speed of sound?
21cm
63cm
½λ = (one football)
= 63 – 21 = 42cm
λ = 0.84m
f = 392Hz
v = λ.f
= (0.84m)(392s-1)
= 329 m/s

49. Open Pipe – open at both ends (antinodes)
HW#12) A bugle can be thought of as an open pipe as shown.
If a bugle were straightened out, it would be 2.65 m long. If the speed
of sound is 343 m/s, find the lowest frequency that is resonant in a bugle.
Find the next higher-resonant frequency in the bugle.

50. Open Pipe – open at both ends (antinodes)
Fund freq: st harmonic:
½λ fits L λ fits L
λ = 2L λ = L
HW#12) A bugle can be thought of as an open pipe as shown.
If a bugle were straightened out, it would be 2.65 m long. If the speed
of sound is 343 m/s, find the lowest frequency that is resonant in a bugle.
Find the next higher-resonant frequency in the bugle.
½λ = L
λ = L
Ch15 HW#3 9 – 13

51. Lab15.2 – Sound Barrier
- due tomorrow
- Ch15 HW#3 due at beginning of period

52. Ch15 HW#3 9 – 13
9. a 440Hz tuning fork is held above a 19cm pipe.
What is speed of sound?
Hz tuning fork resonates in helium at 55cm.
What is the speed of sound?
11. Unknown tuning fork, resonates at spacings of 20.2cm.
Find f.
13. Sax is 65cm long. Find lowest freq cm

53. ½λ = 20.2cm λ = .404m ½λ = 65cm λ = 1.30m Ch15 HW#3 9 – 13
9. a 440Hz tuning fork is held above a 19cm pipe.
What is speed of sound?
¼ λ fits L v = λ.f = (0.76m)(440Hz)
λ = 0.76m =
Hz tuning fork resonates in helium at 55cm.
What is the speed of sound?
¼ λ fits L v = λ.f = (2.20m)(440Hz)
λ = 2.20m =
11. Unknown tuning fork, resonates at spacings of 20.2cm.
Find f.
½λ = 20.2cm
λ = .404m
13. Sax is 65cm long. Find lowest freq cm
½λ = 65cm
λ = 1.30m

54. Ch14,15 Rev 1 – 13
Two ropes are attached. A wave reaches the boundary of the ropes as shown. The wave continues as shown. Which rope is more dense?
2. When 2 waves interfere, is there a loss of energy in the system?
A standing wave is on a string as shown. There are points where it can be touched without disturbing its motion. Explain. How many of these points exist?
4. What happens to the period of a wave as the frequency increases?
5. What happens to the wavelength of a wave as the frequency increases?

55. Suppose you make a single pulse on a stretched spring
Suppose you make a single pulse on a stretched spring. How much energy is required to make a pulse with twice the amplitude?
7. The Sears Tower sways back and forth with a frequency of about
0.10 Hz. What is its period?
8. The frequency of yellow light is 5.0 x 1014 Hz. Find the wavelength of yellow light. (v = 3 x 108 m/s)

56. 9. Sketch the result of the three cases shown, when the centers of the
two wave pulses lie on the dashed line so that the pulses exactly overlap. a. b. c.
You hear the sound of the firing of a cannon 6.0 s after seeing the flash. How far are you from the cannon?
If you shout across a canyon and hear an echo 4.0 s later, how wide is the canyon?

57. 12. A sound wave has a frequency of 9800 Hz and travels along a steel rod. Is the distance between compressions, or regions of high pressure,
is .580 m, what is the speed of the wave?
13. Sound with a frequency of Hz travels through water at a speed of 1435 m/s. Find the wavelength in water.

58. Bonus) In the lab yesterday, a tuning fork with a freq of 512Hz resonated
in a tube of length 16cm. What is the speed of sound?
At what length would it resonate again?
Bonus) Air is blown thru a tube open at both ends, resonating at a fundamental frequency of 256Hz. If the tube is 70cm long, what is the speed of sound there?