Physics 102
		   Homework set 7 Solutions

Chapter 20:

Exercises:

16: The speed does not depend on the frequency or the wavelength.
Thus the speed will not change.  Since wavelength = speed/frequency,
if you double the frequency, the wavelength will halve.

20: The earth tremor and the sound wave are both pressure waves.
Pressure waves travel faster in the ground than in the air because the
ground is a more rigid medium.  Thus, the tremor will travel at faster
speed and reach your feet before the sound wave reaches you ears.

24: a) sound cannot travel in a vacuum.  b) if sound could travel in a
vacuum, it  would still travel much slower than light so that you
would see the explosion long before you heard it.

34: The earphones cancel the jackhammer noise for the operator by
generating sound that is precisely of the correct magnitude and phase
when it reaches the operator's ears.  Thus, the jackhammer's sound is
cancelled only at the operator's ears and only the sound from the
jackhammer is cancelled.  This allows the operator to hear other
sounds clearly.  You cannot hear him, because the jackhammer is making
too much noise.

40: Two frequencies played together generate a 'beat frequency', a
sound wave at the difference between the two frequencies.  We did this
in class where the beat frequency was a few hertz (so we heard the
sound getting louder and softer a few times each second).  If the beat
frequency is high (eg: a few hundred or a few thousand hertz), then we
would hear that as a separate tone.  In this case, we would hear a
sound at 102 kHz - 100 kHz = 2000 Hz.

Problems: 

2: wavelength = speed / frequency = 1530 m/s / 7 1/s = 233 m

4: The sound travels a distance d = v * t = 340 m/s * 0.1 s = 34 m.
This means that it travels 17 m to the wall and 17 m back so the wall
is 17 m away from the bat.

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Chapter 21:
Exercises:

2: wavelength = speed / frequency = 340 m/s / 20,000 1/s = 17 mm
 wavelength = speed / frequency = 340 m/s / 20 1/s = 17 m

8: The wavelength is 60 cm.  You can do this one of two ways: a) the
distance from one node to the next node of a standing wave is 1/2
wavelength.  In this case there is 30 cm from node to node.  b) the
distance from crest to crest in the wave is 15 cm + 30 cm + 15 cm = 60
cm. 

18: The vertical axis on the plots shows the pressure (or amplitude)
of the sound wave.  The horizontal axis shows the time.  The left plot
has more waves per time so it has a higher base frequency, and hence a
higher pitch.  (The right plot has a larger pressure variation so it
is louder.)

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Estimation:

The radius of the Earth (from the inside back cover of the book) is
6.37 * 10^6 m.  Thus the circumference is 2 pi r = 4 * 10^7 m.  At 340
m/s, it takes a time t = distance / velocity = 4 * 10^7 m / 340 m/s =
1.2 * 10^5 s.  

Now we need to convert this to other units:  1.2 * 10^5 s = 2 * 10^3
min = 33 hours = 1 day 9 hours.

Answers within 25% if this one are perfectly acceptable (since I did
not use a calculator and rounded off all my answers).