1. Waves and Sound
You may not realize it, but you are surrounded by waves. The “waviness” of a water wave is readily apparent. Sound and light are also waves with many of the same properties.
Chapter Goal: To learn the basic properties of waves, using sound waves as the example.

2. A wave is a traveling disturbance.
16.1 The Nature of Waves
A wave is a traveling disturbance.
A wave carries energy from place to place.
Most waves travel through a medium, such as air, water, wire, or a Slinky.
Electromagnetic waves (including light) do not need a medium to propagate, and can travel in a vacuum.

3. Longitudinal Waves
Transverse Waves

4. Earthquake Waves
To view this animation, click “View” and then “Slide Show” on the top navigation bar.

5. Transverse Longitudinal
16.2 Periodic Waves
Periodic waves consist of cycles or patterns that are produced over and over again by the source.
In the figures, every segment of the slinky vibrates in simple harmonic motion, provided the end of the slinky is moved in simple harmonic motion.
Transverse Longitudinal

6. In the drawing, one cycle is shaded in color.
“snapshot”
“history”
The amplitude (A) maximum change of a particle of the medium from equilibrium value (may not be zero!). The SI units of amplitude depend on the wave.
The wavelength λ is the horizontal length of one cycle of the wave. SI units are meters.
The period T is the time required for one complete cycle. SI units are seconds.
In the drawing, one cycle is shaded in color.
The left-hand graph shows amplitude vs. displacement.
The right-hand graph shows amplitude vs. time.

7. In the drawing, one cycle is shaded in color.
16.2 Periodic Waves
In the drawing, one cycle is shaded in color.
The frequency f is the number or waves (or cycles) that pass by in a given time. The units are cycles per second, called Hertz (Hz), or s-1
Frequency is the reciprocal of period.
The speed (v) of a wave in m/s can be determined by dividing the wavelength, λ, by the period, T:

8. What is the frequency?
.1 Hz
.2 Hz
2 Hz
5 Hz
10 Hz

9. 2 Waves
The graphs below show amplitude as a function of position (a “snapshot” graph). Both waves travel at the same speed through the same medium. Which wave has the greater frequency?
A. I B. II C. Both have same frequency D. Can’t tell from graph

10. Speed of a wave on a string
The speed at which the wave moves to the right depends on how quickly
one particle of the string is accelerated upward in response to the net
pulling force.
tension in the string
linear density (mass per unit length of string

11. How long is the string?
The mass of a string is 8.00 x10-3 kg, and it is stretched so the tension in it is 220 N. A transverse wave traveling on this string has a frequency of 260 Hz and a wavelength of 0.60 m. What is the length of the string?

12. How long is the string
The mass of a string is 8.00 x10-3 kg, and it is stretched so the tension in it is 220 N. A transverse wave traveling on this string has a frequency of 260 Hz and a wavelength of 0.60 m. What is the length of the string? Ans: 0.885m

13. LONGITUDINAL SOUND WAVES
Sound travels in a longitudinal wave, like a slinky.
The medium can be gas, liquid or solid. We will investigate sound waves traveling in a gas.
Condensation refers to when the air molecules are compressed
Rarefaction refers to when the air molecules are “stretched” apart.

14. 16.5 Wavelength and Frequency
Wavelength: the distance between adjacent condensations (or rarefactions). SI units are meters
Frequency: the number of cycles per second that passes by a given location. Each cycle includes one condensation and one rarefaction.
Pitch (piccolo vs tuba) is an attribute of sound influenced by its frequency

15. Amplitude vs. Distance Graph
The amplitude of a sound wave is expressed in units of pressure (N/m2 ). Condensations are the peaks, with higher-than-atmospheric pressure, rarefactions are the troughs, with lower pressure.
Note the tube shows the sound wave is a longitudinal wave, even though its graph looks like a transverse wave
Loudness is an attribute of sound that depends primarily on the pressure amplitude of the sound wave.

16. Waves transfer energy, not matter.
16.5 Speed of Sound Waves
Waves transfer energy, not matter.
Energy is transferred when individual, vibrating air molecules collide with their neighbors, moving the rarefactions and condensations in the direction of wave travel.

17. The speed of molecules undergoing collisions in an ideal gas such as air is found using principles of Kinetic Theory of gases.
Experiments shows that the speed of air in an ideal gas is:
What do all the variables mean?

18. T - the temperature in Kelvin (Tc + 273)
k - Boltzmann’s constant,
γ (gamma) - ratio of specific heat capacities at constant pressure to that of constant volume Cp/Cv Don’t confuse γ with λ, the constant for wavelength!
γ = 1. 4 (7/5) for air and other diatomic gases.
γ = 1.67 (5/3) for a monatomic gas
m - the mass of a molecule of the gas in kg, a very small number!

19. Sound waves travel through gases, liquids, and solids at considerably
16.6 The Speed of Sound
Sound waves travel through gases,
liquids, and solids at considerably
different speeds.

20. The ultrasonic ruler
An ultrasonic ruler sends out a sound wave which travels to the wall and back. The round trip travel time is 20.0 ms and the air temperature is 32° C. The average molecular mass of air is 28.9 u. What is the distance to the wall?

21. The ultrasonic ruler
An ultrasonic ruler sends out a sound wave which travels to the wall and back. The round trip travel time is 20.0 ms and the air temperature is 32° C. The average molecular mass of air is 28.9 u. What is the distance to the wall? Ans: 3.5 m

22. Speed of sound
Carbon monoxide (CO), Hydrogen gas (H2) and nitrogen (N2) are all diatomic gases that behave as ideal. In which gas does sound travel the fastest at a given temperature?
A. CO B. H2 C. N2

23. The Doppler effect is the change in frequency or pitch
of the sound detected by
an observer because the sound
source and the observer have
different velocities with respect
to the medium of sound
propagation.

24. Doppler Effect Video
Pitch is related to the frequency that you hear. As you listen, pay attention to what happens to the pitch, as opposed to the loudness, of the sound
3:30seconds

25. Dopper Effect Simulation

26. Source moving toward stationary observer
Wavelength perceived by stationary observer is smaller than that perceived by moving source.
o – observer
s – source
v without subscript is the speed of sound in air at 20° C (343m/s) unless otherwise noted
Frequency perceived by stationary observer is larger than that perceived by the moving source.

27. Source moving toward or away from stationary observer
If the source moves towards the observer
If the source moves away, note the frequency heard by the observer will now be less than that that perceived by the source

28. The Opera Singer
An opera singer in a convertible sings a note at 600 Hz while cruising down the highway at 25 m/s. What is the frequency heard by:
a person standing on the sidewalk in front of the car
a person standing on the sidewalk behind the car.

29. The Opera Singer
An opera singer in a convertible sings a note at 600 Hz while cruising down the highway at 25 m/s. What is the frequency heard by:
a person standing on the sidewalk in front of the car: 650 (647) Hz
a person standing on the sidewalk behind the car: 560 (559) Hz

30. Moving observer, stationary source
Observer moving
towards stationary
source will perceive a higher frequency than that perceived by the source
Observer moving
away from
stationary source

31. 16.9 The Doppler Effect
GENERAL CASE – When both source and observer are moving toward/away from/ each other
Numerator: plus sign applies
when observer moves towards
the source
Denominator: minus sign applies
when source moves towards
the observer

32. The Opera Singer Revisited
An opera singer sings a note at 600 Hz in a large outdoor amphitheater. What is the frequency heard by:
a person driving towards her at 25 m/s?
a person driving away from her at 25 m/s.

33. The Opera Singer Revisited
An opera singer sings a note at 600 Hz in a large outdoor amphitheater. What is the frequency heard by:
a person driving towards her at 25 m/s? 644 m/s
a person driving away from her at 25 m/s? – 556 m/s

34. Amy and Zach are both listening to a source of sound waves moving to the right. What frequency does Zach hear relative to the source? a. higher b. lower c. the same
Amy Zach

35. Amy and Zach are both listening to a source of sound waves moving to the right. What frequency does Amy hear, relative to the source? a. higher b. lower c. the same
Amy Zach

36. A B C D

37. Doppler shift question
A red car and a blue car can move along the same straight one-lane road. Both cars can move only at one speed when they move (e.g., 60 mph). The driver of the red car sounds his horn. In which one of the following situations does the driver of the blue car hear the highest horn frequency?
Both cars move apart
Both cars move in the same direction
Both cars move toward each other
Red car moves toward stationary blue car
Blue car moves toward stationary red car.

38. Doppler shift question
A red car and a blue car can move along the same straight one-lane road. Both cars can move only at one speed when they move (e.g., 60 mph). The driver of the red car sounds his horn. In which one of the following situations does the driver of the blue car hear the highest horn frequency?
Both cars move apart
Both cars move in the same direction
Both cars move toward each other
Red car moves toward stationary blue car
Blue car moves toward stationary red car.

39. 16.7 Sound Intensity
Sound waves transfer energy
The amount of energy transported per second (Joules per second) is called the power of the wave.
The sound intensity is defined as the power to area ratio. It is related to (but not the same as!) the loudness of the sound.
The energy released by the source, and therefore the power, are the same, regardless of the distance of the listener.
The sound intensity is proportional to the inverse square of the distance

40. Physical Therapy
Deep ultrasonic heating is used to promote healing of torn tendons (and foot massage?). It is produced by applying ultrasonic sound over the affected area of the body. The sound transducer (generator) is circular with a radius of 1.8 cm, and it produces a sound intensity of 5.9 x 103 W/m2. How much time is required for the transducer to emit 3900 J of sound energy?

41. Physical Therapy
Deep ultrasonic heating is used to promote healing of torn tendons (and foot massage?). It is produced by applying ultrasonic sound over the affected area of the body. The sound transducer (generator) is circular with a radius of 1.8 cm, and it produces a sound intensity of 5.9 x 103 W/m2. How much time is required for the transducer to emit 3900 J of sound energy?
Ans: 649s (my turn next, please!)

42. If the source emits sound uniformly in all directions, the intensity depends
on the distance from the source in a simple way.
Model the area around the sound source as a sphere
The sound intensity is the ratio of power to the surface area of the sphere.
Don’t confuse that with the area of a circle, or the volume of a sphere!
Surface area of sphere

43. Was it as good for you?
Assume that the sound spreads out uniformly and any ground reflections can be ignored. Listener 2 is twice as far from the explosion as Listener 1. If L1 hears with an intensity of 1 W/m2, with what intensity does L 2 hear?
a. 2 b. ½ c. 4 d. ¼

44. Fireworks
I2/I1 = (P/4πr22) = r1 2 /r2 2 , = r2/4r 2
(P/4πr12)
a. 2 b. ½ c. 4 d. ¼

45. Decibels – a measure of loudness
Human hearing spans an extremely wide range of intensities
threshold of hearing at ≈ 1 × 10−12 W/m2
threshold of pain at ≈ 10 W/m2.
To cover a large range, scientists use a logarithmic scale. Sorry about that.
It is logical to place the “zero” of this scale at the threshold of hearing, so I0 = 1 × 10−12 W/m2
We define the sound intensity level, expressed in decibels (dB), as:
Tests show that 1dB is approximately the minimum change in loudness the average human can detect.

46. 16.8 Decibels

47. Example 9 Comparing Sound Intensities
16.8 Decibels
Example 9 Comparing Sound Intensities
Audio system 1 produces a sound intensity level of 90.0 dB, and system
2 produces an intensity level of 93.0 dB. Determine the ratio of intensities. 47

48. Take the antilog of both sides (10x function on most calculators)
16.8 Decibels
β1 = 93 dB, β2 = 90 dB, Find I2/I1
Recall that subtracting log quantities is equivalent to taking the log of their ratio.
Divide both sides by 10 dB
Take the antilog of both sides (10x function on most calculators)
Although I2 is twice that of I1, the sound is not twice as loud. Experimental data show that it takes a 10 dB difference for a sound to be perceived as “twice as loud”. This corresponds to an order of magnitude difference in intensities.

49. 16.11 The Sensitivity of the Human Ear