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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 641Hz . 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 .

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Answer:

from the midpoint we must move 1.34 m to any side and there is no sound

Explanation:

The sound waves are longitudinal waves that can have interference, for this to occur the difference in the path of the waves must be equal to an integer number of half wavelengths for the case from constructive interference and a semi-integer number for destructive interference.

     Δd = 2n  λ/2             constructive interference

     Δd = (2n + ½) λ/2     destructive interference

Where n is an integer

At the midpoint between the two speakers the interference is always constructive, the two distances are equal, so the road difference is zero

Let's calculate the wavelength with the relationship

     v = λ f

     λ = v / f

     λ = 344/641

     λ = 0.537 m

We place the expression for the first destructive interference (no sound)

      n = 1

     Δd = (2 1 + ½) 0.537

     Δd = 1.3425 m

This means that from the midpoint we must move 1.34 m to any side and there is no sound

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