288
.
A microphone is located on the line connecting two speakers that are 0.845 m apart
and oscillating 180° out of phase. The microphone is 2.25 m from the midpoint of the
two speakers. What are the lowest two frequencies that produce an interference
maximum at the microphone’s location?
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The equation that is true for all waves is
f
v
Where in this case, v is the speed of sound.
So,
v
f
The equation that gives us what the problem is looking for is
now telling us to find
.
So, what
kind of physics is involved here?
Interference!
For an interference maximum, as the problem specifies, we set the path length
difference equal to a whole number of wavelengths.
m
Now to our primary mi
2
1
2
1
2
1
ssion, which is to find
.
Let's let the leftmost speaker's distance to the microphone be
,
and the distance from the speaker to its right be
.
So,
0.845m
2.00m
2.4225m.
2
0.8
2.00m
45m
1.5775m.
But wait!
The problem also
2
specifies that the two speakers are oscillating 180
out of phase, which
is
or
out of phase.
Should we fuss and worry about whether to
2
add or subtra
1
2
2
1
ct this to
or
?
Well, as Wednesday said in
"The Addams Family","Does it matter?" So,
2.4225m
1.5775m
0.845m
.
2
2
Well, how about that?
The path length difference (not counting the
"out of phase"part) is the separation distance between the
two speakers!
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 Fall '06
 Alexandrakis
 Physics, Wavelength, NM, 2.25 m, 110 nm, 0.845 meters

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