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.
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.
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.
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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