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Two loudspeakers, A and B, are driven by the same amplifier and emit sinusoidal waves in phase. Speaker B is 12.0 m to the right of speaker A. The frequency of the waves emitted by each speaker is 688 Hz. 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 a point of destructive interference?

Short Answer

Expert verified

The distance, you need to walk, is 0.125 m.

Step by step solution

01

Step-1: Given Data

Distance between speakers: 12m

Frequency emitted: 688 Hz

02

Step-2: Concept applied

For constructive interference the path difference is an integeral multiple of wavelengths and for destructive interference the path difference is a half-integeral multiple of wavelengths.

03

Step-3: Calculation

The wavelength is,

v=λf

where v is the wave velocity, f is the frequency andλis the wavelength of the wave.

role="math" localid="1655809355177" λ=vf=344 m/s688 Hz=0.5 m

To shift from point of constructive interference to the point of destructive interference, the path difference must change by λ/2. If you move a distance x toward speaker B, the distance to B gets shorter by x and the distance to A gets longer by xso the path difference changes by 2x.

2x=λ2x=λ4=0.5 m4=0.125 m

Hence, you must walk0.125m toward speaker B to move to a point of destructive interference.

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