Physics 53
Summer 2010
Quiz 8
Solutions
Check the best answer.
1.
A pipe of length L, open at one end and closed at the other, is supporting
standing sound waves. Which of the following is NOT true?
There is a pressure node at one end and an antinode at the other.
At the open end there is a pressure node.
The frequencies are odd multiples of the fundamental frequency.
√
For the fundamental, λ = 3L . [4L.]
Check T or F depending on whether the statement is true or false.
2.
A piano tuner sounds two adjacent strings for the same note and hears 3 beats/s.
When he increases the tension of the string on the left the beats disappear. The
original frequency of that string was lower than that of the string on the right.
√
T
F
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Physics 53
Summer 2010
3.
3m
a.
Two speakers driven by the same source are arranged as
shown from above. A listener is at the point shown.
Initially the speakers emit sound of frequency 170 Hz.
Take the speed of sound to be 340 m/s.
listener
4m
a.
What is the phase difference between the waves as
they arrive at the listener?
b.
If each speaker separately would result in sound of
intensity I0 at the listener, what intensity does the listener receive with
both speakers active?
c.
As the frequency emitted by the speakers is increased, what is the first
frequency for which the listener hears no sound?
The wavelength is 340/170 = 2 m. The distance from the bottom speaker to the
listener is 5 m (3-4-5 triangle) so the path difference is Δr = 2 m, which is the same
as λ . The phase difference is therefore φ = 2π .
b.
This is constructive interference, so I = 4I0 .
c.
Increasing f decreases λ and therefore increases φ . The next value for destructive
interference is φ = 3π , so kΔr = 3π . This gives λ = 4 /3 m and f = 255 Hz.
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