In a location where the speed of sound is 355 m/s, a 2000 Hz sound wave impinges
ID: 1983145 • Letter: I
Question
In a location where the speed of sound is 355 m/s, a 2000 Hz sound wave impinges on two slits 30 cm apart.(a) At what angle is the first-order maximum located?
Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error.°
(b) If the sound wave is replaced by 5.00 cm microwaves, what slit separation gives the same angle for the first-order maximum?
cm
(c) If the slit separation is 1.00 µm, what frequency of light gives the same first-order maximum angle?
THz
Explanation / Answer
Given
Speed of sound v =355 m/s
Frequency of sound f =2000 Hz
Separation between slits 0.3 m
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(a)we have
=d*sin
maximum => ==v/f=0.1775m
0.1775m=0.3 msin
solve for
=>=36.27 deg
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(b)if =0.05 m
for the same angle
d=/sin=0.08 m=8 cm
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(c)
=d*sin
d=1m
=(1m) sin36.27 deg
=>=5.9*10-7 m
frequency f=c/=5.08*1014 Hz
=508*1012 Hz
=508THz
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