# Sound: waves, intensity and function

1. Feb 17, 2007

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1. The problem statement, all variables and given/known data

Two speakers are 1.8m apart and point to each other. Each is emitting sound at a frequency of 680Hz. The sound waves are propagating at a speed of 340m/s. It can be neglected that the sound intensity is lowering with rising distance from the speaker.

Define the wave functions for the sound emitted by the speakers. By adding those wave functions, find all the points on the line between the speakers where the resulting soundwave has minimum and maximum values of intensity.

Does the point in the middle between the two speaker has a maximum value of sound intensity? If yes why?

Distances s = 1.8m
Frequency f = 680Hz
speed of sound v = 340m/s

Wavelength L = v / f
Wave number k = 2 * Pi / L
Angular frequency w = 2 * pi * f
Amplitude A
Amplitude of pressure Ap

2. Relevant equations

Wave function: A * sin (k * x +/- w * t )

3. The attempt at a solution

P1 = Ap * sin(k * x - w * t + Pi/2)
P2 = Ap * sin(k * (x + 1.8) + w * t + Pi/2)

Now I dont know how I should incorporate the distance between the speakers, so that the sin-value of both functions are equal to Ap at t=0. Further I would somehow take the derivate of the sum of the functions with respect to x to find min/max values. But Im confused on how to set up the two wave functions correctly.

Also I dont know, if the sound has a max value in the middle. Can someone explain this to me?