Vibration, Waves, & Sound
Test Review
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List variables that affect the swing of a pendulum. See Pendulum Lab
Define the period of a pendulum. See Reading Questions
Draw a transverse wave and label the crest, amplitude, wavelength, and trough. See Wave Notes
Draw a longitudinal wave and label the compressions and rarefactions. See Vibration & Wave Reading Questions
Define wave speed in terms of wavelength and frequency. See Wave Notes
What do wave speed, wavelength, and frequency of a sound depend upon? See Wave Notes
Define mechanical and electromagnetic waves. Give examples. See Wave Notes
Describe the Doppler effect. See Doppler Effect Notes
Give the equation for the Doppler effect and how to use it. See Doppler Effect Notes
Be able to determine the speed of a plane from the shock wave it creates. See Worksheet on the back of Loudness and Intensity
Define compression and rarefaction. See Vibration & Wave Reading Questions
What are the frequencies of AM and FM stations? See Sound Reading Questions
What are the two possible units of frequency? See Vibration & Wave Questions
What type of a wave is a sound wave? See Sound Reading Questions
What are the limits of human hearing? See Sound Reading Questions
Define infrasonic and ultrasonic. See Sound Reading Questions
What media transfer sound the quickest? See Sound Reading Questions
Define echo and reverberation. See Sound Reading Questions
Describe the refraction of sound. See Sound Reading Questions
How much energy do sound waves have? See Sound Reading Questions
What happens to sound energy? See Sound Reading Questions
What is a forced vibration? See Sound Reading Questions
What is natural frequency? See Sound Reading Questions
What is resonance? See Sound Reading Questions
Describe what happened to the Tacoma Narrows Bridge. You have to remember this.
Define interference. See Sound Reading Questions
Define beats. See Sound Reading Questions
Define elasticity. See Sound Reading Questions
How does a radio wave differ from a sound wave? See Sound Reading Questions
Describe how you used a resonance tube to measure the speed of sound. See Sound Labs
Describe what tuning forks do to the surrounding medium. See Sound Labs
Describe how to use an echo to measure the speed of sound. See Sound Labs
Describe how the computerized version of a high pitch sound differs from the computerized version of a low pitch sound. See Sound Labs
Describe how the computerized version of an orchestra sounds different from a tuning fork. See Sound Labs
What mediums conduct sound the fastest? See Sound Reading Questions
Which sounds travel further, high pitch or low pitch? See Sound Reading Questions
Define intensity. See Loudness Notes
Give a formula for sound intensity with appropriate units. See Loudness Notes
Define loudness. See Loudness Notes
What is the threshold of hearing? See Loudness Notes
Give the formula with appropriate units for relative intensity. See Loudness Notes
Why is relative intensity a logarithmic scale? See Loudness Notes
Determine relative intensity given sound power and distance from source. See Loudness Notes
Determine intensity given relative intensity. See Loudness Notes
Draw a scaled shock wave for a plane traveling faster than the speed of sound. See worksheet on back of Loudness & Intensity
Determine the speed of a supersonic plane from a scaled drawing. See worksheet on back of Loudness & Intensity
Give a formula for observed frequency based on the Doppler effect with appropriate usage. See Doppler Effect Notes
Determine observed frequencies, source frequencies, observer velocity, and source velocity given the other 3 variables. See Doppler
Effect Notes
Test Review Problems (Use 340 m/s as the speed of sound in air.)
1.
A wave has a speed of 240 m/s and a wavelength of 3.2 m. What are the frequency and period of the wave?
24.0m / s
= 75Hz
λ
3.2m
1
1
T= =
= 0.013sec
f 75Hz
f =
v
=
2.
A piano emits frequencies that range from a low of about 28 Hz to a high of about 4200 Hz. Find the range of wavelengths spanned by this
instrument.
v 340m / s
=
= 12m
f
28Hz
v 340m / s
λ= =
= 0.081m
f
4200Hz
λ=
3.
A sound wave is emitted by the foghorn of a tugboat. An echo is heard 2.6 s later. How far away is the reflecting object?
∆x 2d
=
∆t ∆t
1
1
d = vt = (340m / s)(2.6sec) = 442m
2
2
v=
4.
The note middle C on a piano has a frequency of approximately 264 Hz and a wavelength of 1.31 m. Find the speed of sound in air.
5.
An FM station broadcasts at a frequency of 100 MHz with a radio wave having a wavelength of 3 m. Find the speed of the radio wave.
v = λf = (1.31m)(264Hz) = 346m / s
v = λ f = (3m)(100 x106 Hz) = 3x10 8 m / s
6.
The speed of electromagnetic waves in a vacuum is 3.0x108 m/s. Wavelengths of visible light waves range from about 400 nm in the violet to
700 nm in the red. What is the range of frequencies of light waves? (nanometer =10-9 m)
3x108 m / s
= 7.5x1014 m
λ 400x10 −9 m
v 3x108 m / s
14
= 4.3x10 m
f = =
−9
λ 700x10 m
f =
7.
v
=
A group of hikers hear an echo 3 s after they shout? How far away is the mountain that reflected the sound wave?
∆x 2d
=
∆t ∆t
1
1
d = vt = (340m / s)(3sec) = 510m
2
2
v=
8.
Earthquake S waves have a speed of 3000 m/s. P waves have a speed of 5000 m/s. P waves are detected 2.58 minutes before S waves by a
seismograph. How far is the earthquake's epicenter from the seismograph?
∆t = t s − t p =
d d
−
vs vp

1
1
2.58min(60sec/ min) = d 
−
 3000m / s 5000m /


s
−4
154.8sec = d(1.33x10 sec/ m)
d = 1.16x10 m
6
9.
Calculate the intensity level of a sound wave having an intensity of 10-12 W/m2, 10-11 W/m2, and 10-10 W/m2.
 I
 Io 
 10 −12 W / m 2 
 = 0dB
10 −12 W / m 2 
β = 10 log  = 10log 

 I
 10−11 W / m2 
β = 10 log  = 10log  −12
 = 10dB
 10 W / m 2 
 Io 
 I
 Io 
 10 −10 W / m 2 
 = 20dB
10 −12 W / m 2 
β = 10 log  = 10log 

10. What is the intensity level in decibels of a sound wave of intensity 10-6 W/m2? 10-5 W/m2?
 I
 10 −16 W / m 2 
β = 10 log  = 10log  −12
 = 60dB
 10 W / m 2 
 Io 
 I
 Io 
 10−15 W / m 2 
= 70dB
−12
2
10 W / m 
β = 10 log  = 10log 

11. What is the intensity of a sound whose intensity level is 40 dB? 100dB?
 I
 Io 
β = 10 log 
I


40 = 10 log −12

2
 10 W / m 
4 = log I − log(10
−8
I = 10 W / m
−12
2
W /m )
2
I


100 = 10log  −12

2
 10 W / m 
10 = log I − log(10
−2
I = 10 W / m
−12
2
W /m )
2
12. The area of a typical eardrum is about 5.0x10-5 m2. Calculate the sound power incident on an eardrum at the threshold of hearing.
I=
P
A
P = IA = (10
−12
−5
W / m )(5.0x10 m ) = 5.0x10
2
2
−17
W
13. Repeat the calculation for the threshold of pain which is 120 dB.
I


120 = 10log  −12
 10 W / m 2 
I = 1.0W / m 2
P
I=
A
P = IA = (1.0W / m2 )(5.0x10−5 m2 ) = 5.0x10 −5 W
14. On a work day, the average decibel level of a busy street is 70 dB with 100 cars/minute. If the number of cars is reduced 25 cars every minute
on a weekend, what is the decibel level of the street?
 I

70dB = 10 log −12100cars 2 
 10 W / m 
−5
I100cars = 10 W / m
2
I75cars = .75(10 −5 W / m 2 ) = 7.5x10−6 W / m 2
−6
 .5x10 W / m 
 = 69dB
 10−12 W / m 2 
β = 10 log
2
15. A rather noisy typewriter produces a sound intensity of 10-5 W/m2. Find the decibel level of this machine and calculate the new decibel level
when a second identical typewriter is added to the office.
 I
 Io 
 10 −5 W / m 2 
−12
2  = 70dB
10 W / m 
 I
 Io 
 2x10 −5 W / m 2 
= 73dB
−12
2 
10 W / m 
β = 10 log  = 10log 

β = 10 log  = 10log 

16. A small source emits sound waves with a power output of 80 W. Find the intensity 3 m from the source.
I=
P
P
80W
2
=
2 =
2 = 0.71W / m
A 4πr
4π (3m)
17. For the sound in the previous problem, find the distance at which the sound level is 40 dB.
I


40 = 10 log  −12
2
 10 W / m 
P
I = 10 −8 W / m 2 =
4π r 2
1
80W
r=
= 25, 231m
2 π (10 −8 W / m 2 )
18. A train moving at a speed of 40 m/s sounds its whistle, which has a frequency of 500 Hz. Determine the frequency heard by a stationary
observer as the train approaches.
v 



1± o
1


v  = 500Hz
fo = fs 
= 567Hz

vs 
40m / s 
1 ∓ 
1 −



v
340m / s 
19. An ambulance travels down a highway at a speed of 75 mi/h, its siren emitting sound at a frequency of 400 Hz. What is the frequency heard by
a passenger in a car traveling at 55 mi/h in the opposite direction as the car approaches.
miles
hour
miles
55
hour
1610m 1hour
x
= 33.5m / s
mile 3600sec
1610m 1hour
x
x
= 24.6m / s
mile 3600sec
v 
 1 + 24.6m / s 

1± o


340m / s 
v
fo = fs 
vs  = 400Hz 
33.5m / s  = 476Hz
1 ∓ 
 1−



v
340m / s 
75
x
20. What frequency is heard by the car after it passes and moves away from the ambulance?
24.6m / s 
v 


1−
1± o

340m / s 
v  = 400Hz 
fo = fs 
= 338Hz

vs 
33.5m / s 
1 ∓ 
 1+



v
340m / s 
21. A train at rest emits a sound at a frequency of 1000 Hz. An observer in a car travels away from the sound at a speed of 30 m/s. What is the
frequency heard by the observer?
30m / s 
v 


1−
1± o

340m / s 
v  = 1000Hz
fo = fs 

 = 912Hz
vs 
1
1 ∓ 





v
22. The observer in the previous problem stops the car. Determine the frequency she hears when the train approaches her at a speed of 30 m/s
and when the train recedes from her at a speed of 30 m/s.
v

1± o
v
fo = fs 
vs
1 ∓

v



1

 = 1000Hz
= 1098Hz


30m / s 

1 −



340m / s 
v

1± o

v
fo = fs 
vs
1 ∓

v



1



 = 1000Hz
30m / s  = 919Hz

1 +



340m / s 
23. An alert physics student stands beside the tracks as a train rolls slowly past. She notes that the frequency of the train whistle is 442 Hz when
the train is approaching her and is 441 Hz when the train is receding from her. What should this alert physics student determine the speed of
the train to be?
v 

1± o

v
fo = fs 
v 
 1 m s 
v




1
1




442Hz = fs 
 and 441Hz = fs 

vs
vs
 1 −

 1 +

340m / s
340m / s 


1


fs 

vs
1−



442Hz
340m / s 
=
441Hz


1


fs 

vs
 1 +

340m / s 
vs
340m / s
1.00227 =
vs
1−
340m / s
vs
vs


= 1+
1.00227  1 −


340m / s 
340m / s
340.77098 − 1.00227vs = 340 + vs
1+
0.77098 = 2.00227vs
vs = 0.3851m / s