1. Sound

2. Sound Waves Mechanical Waves (require a medium) Longitudinal waves
Formed by a series of compressions and rarefactions.

4. Frequencies of Sounds Infrasonic Sound (elephants can hear)
f < 20 Hz
Audible Sounds
(humans can hear)
20 – 20,000 Hz
Ultrasonic Sound
(dolphins can detect)
f > 20,000 Hz
Increasing Frequency

5. Pitch
How high or low we perceive a sound to be, depending on the frequency of the sound wave.
As the frequency of a sound increases, the pitch of that sound increases.
Which graph represent the sound with the highest pitch? C A B C
What is wrong with these graphs representing sound waves?
Sound is longitudinal, not transverse.

6. Ultrasound
Images produced by ultrasonic sound show more detail then those produced by lower frequencies.
Ultrasonic sound has many applications in the field of medicine.
Ultrasound images, such
as the one shown here, are
formed with reflected sound
waves.

7. Amplitude
The amplitude of a sound wave corresponds with how loud the sound is.
A large amplitude is a loud sound.
A small amplitude is a quiet sound.

8. Practice Draw a loud and high pitched wave.
Draw a loud and low pitched wave.
Draw a quiet sound wave with medium pitch

9. Wave Speed Activity

10. Speed of sound depends on medium and temperature.
V (m/s)
Gas: air (0oC)
331
Gas: air (25oC)
346
Gas: air (100oC)
366
Liquid: water (25oC)
1490
Solid: copper (density = 8.96g/cm3)
3560
Solid: aluminum (density = 2.70g/cm3)
5100
Source: Serway/Faughn, p. 461 (Table 14.1)

11. To calculate the speed of sound through air at different temperatures…
331 m/s is the speed of sound at 0oC
T = temperature in Kelvin
Remember: Kelvin = oC + 273

12. Sound waves propagate in 3D
Sound waves travel away from a vibrating source in all directions.
In these spherical waves, the circles represent compressions (wave fronts).
Source
Wave front l

13. Intensity
Intensity (I) of a wave is the rate at which energy flows through a unit area (A) perpendicular to the direction of travel of the wave.

14. However, power is also the rate at which energy is transferred (W = J/sec)
And sound waves are spherical, so the power is distributed over the surface area of a sphere (4pr)
I = Intensity (W/m2)
P = Power (W)
R = Distance from source (m)

15. What is the intensity of the sound waves produced by a trumpet at a distance of 3.2 m when the power output of the trumpet is 0.20 W?

16. Equations:
Intensity is the rate at which energy flows through the surface, DE/Dt, divided by the surface area, A.
HIDDEN
This is to say ….
Units: watts/m2, W/m2

17. For spherical waves centered on the source…
HIDDEN
To compare the sound intensities at different distances, use this equation:

18. Human Hearing - Frequency
The range of human hearing is generally considered to be from about 10 Hz to about 20,000 Hz.
In reality, it’s much worse.
Few people can hear above
14-15 thousand Hz, and it gets
worse as you grow older.

19. Human Hearing - Intensity
Hearing also depends on the intensity of the sound.
The softest sound that can be heard by the human ear has an intensity of 1x10-12 W/m2. This intensity is said to be the Threshold of Hearing.
The loudest sound the human ear can tolerate has an intensity of 1.0 W/m2. This is known as the Threshold of Pain.

20. Human Hearing - Decibles
When dealing with human hearing, the intensity range is very large (1x10-12W/m2 to 1 W/m2).
A sound with twice the intensity, isn’t heard as twice as loud.
The ear works on a logarithmic scale.
Sound loudness is measured in decibels (dB) which compare the sound’s intensity to the intensity at the threshold of hearing.

21. Conversion of intensity to decibel level
Decibel (dB)
Example
1x10-12
Threshold of hearing
1x10-9 30
Whisper
1x10-7 50
Normal Conversation
1x10-4 80
Traffic
1x10-2
100
Fire Engine
1x10
120
Rock Concert
1x102
140
Jet

22. Decibels and Intensity
When the intensity is doubled (one person talking vs two people talking) there is a three decibel increase.
When the intensity is ten times as large there is a ten decibel increase and the noise sounds twice as loud.

23. Relative Loudness – Decibels (dB)
HIDDEN
Decibels are designed for talking about numbers of greatly different order of magnitudes.
Such as….1 and
For convenience the RATIO between the two numbers is converted into a logarithm. Logarithms are used because the human ear responds to sound roughly in a logarithmic manner.

24. Two machines would be 73 dB
Example: A rather noisy typewriter produces a sound intensity of 1 x 10-5 watts/m2 which is 70 dB. Find the decibel level when a second identical machine is added to the office.
Two machines would be 73 dB

25. Calculating Decibel Level:
= 10 log (I/Io) = 10 log (I/1x10-12)
Where: Io is the threshold of hearing (1x10-12 W/m2)
and b is the decibel level
Thus…
Threshold of hearing 0dB
Threshold of pain 120 dB
Doubling the sound intensity is a 3 dB increase.

26. 80 dB

27. 100 dB

28. 120 dB

29. 140 dB

30. Example: Michael wants to install a 100
Example: Michael wants to install a 100. W stereo amp in his sweet new VW. What will the dB level be, at his ears, approximately 1.50 m away from the speakers?  
= 125 dB
Note this is three and a half times the threshold of pain.

31. Waves & Movement
the
Doppler Effect

32. The Doppler Effect
Relative motion between the source of waves and the observer creates a change in frequency.
See:
Non-Java applet:

34. Doppler Effect Equation:
fd Perceived frequency heard by the detector
fs Frequency being created by the source.
* Define the + direction to be from the source to the detector
vd velocity of the detector
vs velocity of the source.
V velocity of sound

35. Doppler effect possibilities:
Highest frequency +
+ Vs - Vd +
+ Vs + Vd
Lowest frequency +
- Vd - Vs +
+ Vd - Vs

36. Imagine sitting inside a car. The car’s horn has a frequency of 500 Hz
Imagine sitting inside a car. The car’s horn has a frequency of 500 Hz. What frequency would you hear inside the car, moving at 25 mi/hr?
500 Hz

37. Imagine yourself outside the car
As the car approaches you, is the frequency higher or lower then 500 Hz?
As the car passes and leaves you behind, is the frequency higher or lower then 500 Hz?

38. HEAR DOPPLER CAR

39. Example: An ambulance moving at 25 m/s drives towards a physics student sitting on the side of the road. The EMTs in the ambulance hear the siren sounding at 650 Hz. What is the frequency heard by the student? (assume speed of sound is 343 m/s) +
fs = 650 Hz fd = ?
Vs = + 25m/s Vd = 0 m/s

40. Wow, the bike rider is invisible!
Example: At rest a car’s horn sounds the note A (440 Hz). While the car is moving down the street, the horn is sounded. A bicyclist moving in the same direction with 1/3 the car’s speed hears a lower pitched sound. (A) Is the cyclist ahead of or behind the car?
The observed frequency is lower than the actual frequency, therefore they must be moving apart from one another. This means the cyclist is behind the car because he is moving slower than the car.
Wow, the bike rider is invisible!

41. (B) If the car is moving at 33 m/s (with a horn frequency of 440 Hz) and the bike is following the car at 11 m/s, what is the frequency detected by the bicyclist? (assume speed of sound is 343 m/s) +
fd = ? fs = 440 Hz
Vd = - 11m/s Vs = - 33 m/s

42. Supersonic Movement

45. Beats

46. Beats

48. Guitars can be tuned using beats -- tune to “zero beat frequency”

50. Beats
The frequency of the resulting beats can be calculated by:

51. A certain piano key is suppose of vibrate at 440 Hz
A certain piano key is suppose of vibrate at 440 Hz. To tune it, a musician rings a 440 Hz tuning fork at the same time as he plays the piano note and hears 4 beats per second. What frequency is the piano emitting if the note the piano plays is too high?
4 Hz = f
f1 = 444 Hz
4 Hz = f2
f2 = 436 Hz

52. Beats can also occur from two sources playing the same frequency

53. Along the yellow lines there is destructive interference
Along the yellow lines there is destructive interference. There is no wave disturbance there.
Constructive Interference
Destructive Interference

54. Interference from two sources at the same frequency:
HIDDEN
Constructive Interference:
r2-r1 = nl
Destructive Interference:
r2-r1 = (n + ½)l
r1 & r2 = path length
r2-r1 = path length difference
l = wavelength
N = integer number of wavelengths

55. Constructive Interference (n=0)

56. Constructive Interference (n=1)

57. Destructive Interference (n=0)

58. Destructive Interference (n=1)

59. Example: A person walks back and forth near a pair of speakers
Example: A person walks back and forth near a pair of speakers. The person starts at point O, directly between the speakers and then walks to point P which is where they hear the first minimum in sound intensity. a. What type of interference is occurring at point P? b. At point P the person is 8.08 m away from speaker 1 and 8.21 m away from speaker 2. What is the wavelength of the sound being played? c. What is the frequency of the sound? (speed of sound in air is 343 m/s) O P
0.350 m
3.00 m
8.00 m r1 r2

60. f = 1,320 Hz or = 1.32 kHz r1 = 8.08 m r2 = 8.21 m Vsound = 343 m/s
At point P there is minimum sound intensity so at point P there must be destructive interference.
Vsound = 343 m/s
f = ?
f = 1,320 Hz
or = 1.32 kHz
 = 0.26 m
b. At point P the person is 8.08 m away from speaker 1 and 8.21 m away from speaker 2. What is the wavelength of the sound being played? c. What is the frequency of the sound? (speed of sound in air is 343 m/s)

61. Standing Waves
Wave pattern that results when two waves of the same f, l, and A travel in opposite directions and interfere.
The resultant of the two waves appears to be standing still.

62. Resonance
The tendency of a system to vibrate with maximum amplitude at a certain frequency.
When a system is in resonance, a small input of energy leads to a large increase in amplitude.
Examples: being pushed on a swing.
Tacoma Narrows Bridge

63. Example: Blowing over a bottle of water will produce resonance.
The water stops the sound so it is a node.
The air is free to move at the top of the bottle, so it is an antinode.
Going from node to the first antinode, is ¼ of a wave.
Therefore, the length of the bottle is ¼th the wavelength.

64. Example: Blowing over a bottle of water will produce resonance
Example: Blowing over a bottle of water will produce resonance. If the column of air in the bottle is 16.0 cm long, what is the resonant frequency of the bottle? (assume vsound = 343 m/s)

65. Resonance in a Tube  = 4L L = 9.00 cm
Tuning fork with frequency of 958 Hz
Length of tube out of the water = ?
Assume the speed of sound is 345 m/s.
There is a quarter of a wave in the tube.
 = 4L
L = 9.00 cm

66. Harmonics
Sometimes more than one size wave will fit the given parameters (node or antinode at the end). These different wave sizes are called harmonics.
First harmonic (or fundamental frequency) is the largest wave that fits the parameters.
Second harmonic (first overtone) is the second largest wave that fits the parameters.

67. Tube with two sides open Example: Flute
Fundamental frequency
(first harmonic)
L = ½ l
Second Harmonic
(First Overtone)
L = l
Third Harmonic
(Second Overtone)
L = 3/2 l or 1 ½ l

68. Tube with one side open & one side closed Example: - Blowing over the top of a bottle - Panpipes
Fundamental frequency
(first harmonic)
L = ¼ l
Second Harmonic
(First Overtone)
L = ¾ l
Third Harmonic
(Second Overtone)
L = 5/4 l or 1 ¼ l

69. Tube with both sides closed or String held on both ends
Tube with both sides closed or String held on both ends. Example: Guitar, harp, piano, violin
Fundamental frequency
(first harmonic)
L = ½ l
Second Harmonic
(First Overtone)
L = l
Third Harmonic
(Second Overtone)
L = 3/2 l or 1 ½ l

70. Good applet on harmonics: