Two small speakers A and B are driven in step at 720Hz by the same audio oscillator

Two small speakers A and B are driven in step at 720Hz by the same audio oscillator. These speakers both start out 4.50m from the listener, but speaker Ais slowly moved away.

Part A:
At what distance d will the sound from the speakers first produce destructive interference at the location of the listener?

Part B:
If A keeps moving, at what distance d will the speakers next produce destructive interference at the listener?

Part C:
After A starts moving away, at what distance will the speakers first produce constructive interference at the listener?

Expert Solution

In air, the wavelength of 725Hz is about 0.47m.
So speaker A is 180° out of phase at 4.5+0.235= 4.735m and again at 4.5+0.47+0.235=5.205m.
Speaker A is in phase at 4.5+0.47=4.97m

However those are the simple answers. As the speaker moves away, it gets quieter and anything between 90° and 270° is "destructive" wrt the vector at B, or120° to 240° wrt the total absolute value < B alone, so
1. the FIRST destructive interference is at >90° or >120°, not at 180°
2. the maximum destructive interference is slightly before 180° because the distance is also reducing the absolute value.

genius_generous answered 2 years ago

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