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## Homework Statement

Two identical loudspeakers are located at points A & B, 2m apart. The loudspeakers are driven by the same amplifier (coherent and are in the same phase). A small detector is moved out from point B along a line perpendicular to the line connecting A & B. Taking speed of sound in air as 332 m/s, find the frequency below which there will be no position along the line BC at which destructive interference occurs.

## Homework Equations

## The Attempt at a Solution

I am not sure how would I approach this problem. I started with calculating the path difference when the detector is at a distance x from its initial position,

[tex]\Delta x=\sqrt{4+x^2}-x[/tex]

For destructive interference,

[tex]\sqrt{4+x^2}-x=\left(n+\frac{1}{2} \right)\lambda[/tex]

where ##\lambda## is the wavelength of the wave.

I don't know how should I proceed from here.

Any help is appreciated. Thanks!