Two identical speakers are pointed at one another, along the x-axis. The speaker

Question

Two identical speakers are pointed at one another, along the x-axis. The speakers, which are in phase with one another, broadcast identical sound waves at a frequency of 170 Hz. Assume the speed of sound to be 340 m/s. Speaker A is positioned at x = 0, and speaker B is located at x = +4.20 m. (a) In between the speakers, there are a few locations at which the two waves produce completely destructive interference. What is the x-coordinate of the point closest to speaker B at which completely destructive interference occurs? m (b) In between the speakers, there are also a few locations at which the two waves produce completely constructive interference. How many locations are there, along the line between the speakers, at which completely constructive interference occurs? locations

Explanation / Answer

Note that the speakers produce a wavelength of 2 m.

Let x = that coordinate

Thus,

(4.2 - x) - x = (n + 1/2) (2 m)

If n = 0,

x = 1.6 m

If n = 1,

x = 0.6 m

If n = -2

x = 3.6 m   [ANSWER, closest to speaker B]

**********************

Let x = that coordinate

Thus,

(4.2 - x) - x = (n) (2 m)

Which happens only when n = -2, -1, 0, 1, 2.

Thus, there are 5 LOCATIONS. [ANSWER]

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