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Two sound waves of the same frequency and amplitude are broadcast from speakers at opposite ends of a theater. In the middle of the theater, you hear no sound. Which of the following is true The two waves are in phase in the middle of the theater. The two waves are 45° out of phase in the middle of the theater. The two waves are 90° out of phase in the middle of the theater. The two waves are 180° out of phase in the middle of the theater.

Kristi Hammond

in Physics

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Nicholas Rivera on May 30, 2018

The last one is true.Let's say that wave 1 is the function W1 = a*sin(w*t), and a second W2 = A*(w*t - 180)both waves have the same amplitude and the same frequency (w=2*pi*f)at t=0 the first wavelength has a value of 0, and the second has a value of 0. Their sum is equal to 0.As the time begins to pass from the first wave of value will grow, while the second will decrease and negative (due to the shape of the sine function). Both of them are changing its value at the same speed due to the same frequency, and their sum will always be 0. Verification of the graph.


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