Can somebody help me understand what “resonant frequency” is?

Question

Can somebody help me understand what “resonant frequency” is?

In: Physics

Answer 1

Suppose you’re in a very long hallway, closed at both ends, and when you shout something, you hear an echo bounce back at you from the far end of the hallway. It takes exactly 1 second for the sound to travel from you, to the far wall, and back again. And since there’s another wall behind you, it bounces back a second time and you hear another, weaker, echo another second later and so on.

Now, suppose you decide you want to shout *along* with your echo. So you say “Boo!” and one second later, when your “Boo!” bounces back at you, you shout “Boo!” again. And since your timing is *so amazing*, you manage to say it sound-for-sound, waveform-for-waveform exactly the same as you did the first time. And then something cool happens: your voice *combines* with the echo, to create a louder “boo” than you started with! And when it bounces back again, you say “boo” again, stacking up a *third* boo, making it even louder! You keep doing this until the sound bouncing back and forth is deafening. Windows break, the roof collapses, etc.

This works, because you chose the right timing, the right *frequency*, to shout ‘boo’ at. If you instead had decided to shout ‘boo’ every 0.71294 seconds, then the echoes would not have coincided with each other, and this stacking effect would not happen.

We say that the hallway has a resonant frequency of 1 Hertz, or one cycle per second, because ‘1 per second’ is the right frequency to get this stacking effect. This resonant frequency is determined by length of the hall and the speed of sound.

Something that’s worth being aware of: if you had decided to shout boo every *half* second, it would still work, because every boo’s echo will overlap with the second-next boo. And same for thirds of a second, or fourths of a second. But 0.71294 wouldn’t work, would it? Can you see why? This effect, where shouting boo at 2x or 3x or 4x the resonant frequency *also* works to produce resonance, is called the harmonic series.