How Can You Cancel Out Sound?
The key to sound waves is that the result of your ear is the sum of all the sound waves hitting your ears at the time. If you are listening to a band, even if you may hear several different sources of sound, the pressure waves that hit your eardrum will add up, so your ear drum only feels one pressure at any given moment.
Now comes a cool part: it is possible to produce a sound wave that is exactly the opposite of another wave. This is the basis for the noise-cancelling headphones you may have seen. Take a look at the picture below. The top and second waves are pure tones. If the two waves are in phase, they add a wave of the same frequency but twice the amplitude. This is called constructive interference. But, if they are exactly out of phase, they add up to zero.This is called destructive interference. When the first wave is at its maximum pressure, the second wave is at its minimum. If both of these waves hit your ear drum at the same time, you would not hear anything because the two waves always add up to zero.
How sound waves add and subtract
In the next section, we'll see how the muffler is designed to create waves that cause as much destructive interference as possible.