Calculate Max Wavelength of Sound Emitted by Loudspeakers

[Peter G.]

Hi,

Two loudspeakers are connected to the same audio oscillator. An observer walks in between them. At a point M, halfway between the speakers he hears a loud sound. By the time he gets to a point P 2m away from M he hears no sound at all. Calculate the maximum wavelength of sound emitted by the loudspeakers.

This is what I did:
If 2 m there is no sound at all, there is destructive interference, hence: (n + 1/2) λ = 2.

The maximum wavelength would be equal to 4, but the book says 8 m. How?

Thanks,
Peter G.

 

[PeterO]

Hi,

Two loudspeakers are connected to the same audio oscillator. An observer walks in between them. At a point M, halfway between the speakers he hears a loud sound. By the time he gets to a point P 2m away from M he hears no sound at all. Calculate the maximum wavelength of sound emitted by the loudspeakers.

This is what I did:
If 2 m there is no sound at all, there is destructive interference, hence: (n + 1/2) λ = 2.

The maximum wavelength would be equal to 4, but the book says 8 m. How?

Thanks,
Peter G.

In between the speakers, you have a standing wave pattern, and indeed the 4m is the wavelength of the standing wave pattern, however the wavelength of the traveling waves that caused the Standing wave pattern is twice as long as the standing wave.

 

[Peter G.]

Oh, ok. I haven't studied Standing Waves yet and the exercise is before that part, but maybe the book assumed I had that knowledge.