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PRACTICE PHYSICS 101 EXAM
Problem 1
I.
A student, holding a 500 Hz tuning fork, is walking at 1.50 m/s on a
direct line between two parallel smooth reflecting walls. What
frequency of sound are heard by the student?
Answer
At the wall the student approaches,
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
=
s
v
v
v
f
f
'
because the wall is a
stationary “observer” watching a moving source.
For the sound reflected by the wall, the wall is a stationary “source”
that reflects the same frequency it “hears”, and the student is a
moving observer, so if the student hears frequency f’’, where:
Hz
s
m
s
m
s
m
s
m
Hz
v
v
v
v
f
v
v
v
f
f
s
o
o
4
.
504
/
5
.
1
/
341
/
5
.
1
/
341
500
'
'
'
=
⎟
⎠
⎞
⎜
⎝
⎛
−
+
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
+
=
⎟
⎠
⎞
⎜
⎝
⎛
+
=
Similarly, for receding wall, (the student is going away from the wall,
the velocities have inverse signs):
Hz
s
m
s
m
s
m
s
m
Hz
v
v
v
v
f
f
s
o
6
.
495
/
5
.
1
/
341
/
5
.
1
/
341
500
'
'
=
⎟
⎠
⎞
⎜
⎝
⎛
+
−
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
+
=
II.
A column of air in a tube is found to have standing waves at
frequencies of 380, 532 and 684 Hz. There are no standing wave
frequencies between the above frequencies.
a)
What is the fundamental frequency of the tube?
Answer
Resonant frequency for sound waves in a tube are uniformly spaced.
Notice the frequency spacing here is 152 Hz because 684Hz-
532Hz=532Hz-380Hz=152Hz. Keep subtracting multiples of 152Hz
until you reach a frequency <152Hz and you’ll reach the fundamental
frequency f
fundamental
=76Hz.
b)
Is the tube open at both ends or open at one end and closed
at the other end?
Answer
For a tube open at both ends, the fundamental frequency is the same
as the frequency of spacing. For a tube closed at one end, the
fundamental frequency is on half of the frequency of spacing. The
latter is true, so the tube is closed at one end.

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