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Writer's picturekeshprad

PhysicsBowl 2019 Q39


39) Speaker A is placed 1 meter from point P and Speaker B is placed 0.75 meters from Speaker A as shown. We want to find how much further Speaker B should be moved in order to create a maximum sound intensity.


Using the wave equation, we can find the wavelength of the sound waves.

Where v is velocity, f is frequency, and λ is wavelength

In order to achieve the maximum constructive interference, we want the wave's phase difference to be a multiple of the wavelength. We can write this into a formula.

Where d[A] is distance from speaker A to point P, d[B] is distance from speaker B to point P, λ is wavelength, and m is a constant

Since we want maximum constructive interference, m must be a whole number. For example, a setup where m is 1 would result in maximum sound intensity; however, a setup where m is 0.5 would result in minimum sound intensity.


Additionally, the problem says that we want to record the first maximum, which means m must be 1 and cannot be any other whole number. Other than this, we know that d[A] must be 1 meter because speaker A is in a fixed position as shown in the given diagram.

Where d[A] is distance from speaker A to point P, d[B] is distance from speaker B to point P, λ is wavelength, and m is a constant

This is not our final answer; this is the distance from speaker B to point P. Remember that the question asks for how much further, speaker B should be moved in order to find the maximum sound intensity. We can use the Pythagorean theorem to find this.

Answer: A

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