Two loudspeakers, A and B, are driven by the same amplifier and emit
sinusoidal waves in phase. The frequency of the waves emitted by each
speaker is 624 Hz . You are standing between the speakers, along the
line connecting them and are at a point of constructive interference.
How far must you walk toward speaker B to move to reach the first point
of destructive interference?
Take the speed of sound to be 344 m/s.
Two loudspeakers
2012-12-01 12:44 am
回答 (2)
2012-12-01 9:16 am
✔ 最佳答案
Let L be the separation between the two loudspeakers A and B, and d be the distance between the observer (i.e. you) and louspeaker A. Hence, the distance between the observer and loudspeaker B = (L - d)The condition for constructive interference is:
path difference = m入
where m is a positive integer and 入 is the wavelength.
Hence, d - (L - d) = m入
i.e. 2d - L = m入 -------------------- (1)
The condition for destructive interference is:
path difference = (m + 1/2)入
Suppose the observer walks a distance x towards louspeaker B,
the new distances of the observer from A and B are respectively (d + x) and (L - d -x).
hence, path difference = (d+x) - (L-d-x) = 2d + 2x - L
thus, 2d + 2x - L = (m + 1/2)入 -------------- (2)
(2) - (1): 2x = 入/2
i.e. x = 入/4 = (344/624).(1/4) m = 0.1378 m
2012-12-01 1:59 am
A You B
delta = 0.5 lambda
and you will get destructive interference.
so you should walk 0.5 lambda to B.
lambda= v / f=344/624
0.5 lambda= ans.
delta = 0.5 lambda
and you will get destructive interference.
so you should walk 0.5 lambda to B.
lambda= v / f=344/624
0.5 lambda= ans.
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