# Sound waves

## Main Question or Discussion Point

When sound waves of the same frequency interact, they amplify. Sound waves of different frequencies cancel each other out. Where does the energy go when they cancel?

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rbj
i don't think i even agree with your premise enough to consider an answer.

in an ideal gas (one that is much warmer than its boiling point) of which our air is pretty close to, sound waves interfere (simply add, or superimpose). sound waves of the same frequency can team up, if they are in-phase and can completely cancel, if they are outa phase by 180o and equal amplitudes. if they are of different frequencies, they do not cancel.

if two sound waves that are the same frequency (and are synchronized) but have sources placed in different positions, at some locations in the field, they are outa phase and they cancel. at other positions, they are in-phase and team up. i guess the energy from the cancellations goes to where they team up.

berkeman
Mentor
When sound waves of the same frequency interact, they amplify. Sound waves of different frequencies cancel each other out. Where does the energy go when they cancel?
As rbj says, your question is not quite accurate. A better way to ask would be "Where does the sound wave energy go at constructive interference nodes?" Just like with standing waves on a string, where you get some parts of the string swinging up and down with maximum amplitude ("antinodes"), and some locations where the string is not moving up and down at all ("nodes"). For the string, the answer to the question "How do the left-propagating and right-propagating waves move through the non-moving nodes?" is that the *tension* in the string at the nodes is what propagates the waves. The string does not need to be moving up and down there in order to propagate the energy that results in the up-down movement of the rest of the string.

String waves are "transverse", meaning that the motion of the string is perpendicular to the direction of propagation of the wave on the string. Sound waves are longitudinal, meaning that the oscillating motion of the air molecules is parallel with the direction of the sound wave travel. So, when you get a node in the superposition of two equal-frequency sound waves from separated sources, I would guess that the energy is tranferred through the nodes still with oscillating air pressure waves, but the local addition sums to zero (so you hear nothing). The waves still exist and pass by each other, since sound waves do not interact with each other in linear media like air. It's just that the sum of them is zero at the point where you are listening....

Obviously I could not have meant that all different sound waves cancel each other, if that was the case, you would only be able to hear one frequency at a time. What I meant was that sometimes sound waves cancel, and where does that energy go? My assumption was that when they team up, more air is moved, and when they cancel less is moved, or should I say compressed?. Is that wrong?