Suppose we had two speakers, one placed some distance directly behind the other

Question

Suppose we had two speakers, one placed some distance directly behind the other and both pointing along the same direction, facing us. Now, we connect the speakers to the same source and turn them on producing a single continuous tone of 440 Hz. If the speed of sound in air is about 343 m/s, then how far would we have to put the back speaker behind the front one so that we never hear the tone when standing anywhere directly in front of the speakers? What is the difference in angles, Delta theta, between the m^th and (m + 1)^th bright fringes? Show further that if theta_m and theta_m + 1

Explanation / Answer

1.
We will not hear the tone, if there is destructive interference that is path difference = lambda/2

so,
distance must be equal to lambda/2

lambda = v/f = 343/440 = 0.78 m

distance = lambda/2 = 0.78/2 = 0.39 m
Answer: 0.39 m

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