If two sound waves undergo complete destructive interference, what must be true?

A. They have the same amplitude. B. They have the same frequency. C. They are 180° out of phase. D. all of the above

all are true.

All of these

To determine the correct answer, let's first understand the concept of destructive interference between sound waves.

Destructive interference occurs when two sound waves meet and interact in a way that causes their amplitudes to cancel each other out, resulting in a decrease or complete elimination of sound. This happens when the crests of one wave align with the troughs of the other wave.

Now, let's consider the options provided:

A. They have the same amplitude: This statement is partially correct. For destructive interference to occur, the amplitudes of the two waves must be equal. However, having the same amplitude is not the only requirement for destructive interference to happen.

B. They have the same frequency: This statement is not necessary for destructive interference. The frequency of the sound waves does not affect whether or not destructive interference will occur. It is possible for two sound waves with different frequencies to still undergo destructive interference if the conditions for cancellation of amplitudes are met.

C. They are 180° out of phase: This statement is correct. For destructive interference to take place, the two sound waves must be 180° out of phase, meaning that the troughs of one wave align with the crests of the other wave. This phase shift plays a crucial role in canceling out the amplitudes of the waves and causing destructive interference.

Therefore, the correct answer is C. They are 180° out of phase.