1. Two speakers, one directly behind the other, are each generating a 210-Hz sou

Question

1.

Two speakers, one directly behind the other, are each generating a 210-Hz sound wave. What is the smallest separation distance between the speakers that will produce destructive interference at a listener standing in front of them? The speed of sound is 335 m/s.

2.

Loudspeakers A and B are vibrating in phase and are playing the same tone, which has a frequency of 491 Hz. They are set up as in the figure, and point C is located as shown there. The distance between the speakers and the distance between speaker B and point C have the same value d. The speed of sound is 343 m/s. What is the smallest value of d, such that constructive interference occurs at point C?

Explanation / Answer

1)

The wavelength ? of the sound is v/f = 335/210 = 1.595m

Now let x be the separation distance of the speakers

When the path distance is ?/2 there is destructive interference

So the path difference is also x so x = ?/2 = 1.595/2 = 0.7976m

2)

d will be minimum for n=1

wavelength = 343/491 = 0.6986 m
For constructive interference, d*sqrt(2) = n(lambda)

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