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



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

In: Physics

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.

If you drop a stone in a pool of water you don’t just get one ripple. The first one is big but you get a lot of smaller ones moving outwards (propagating) behind it. These smaller ripples are resonant frequencies, they aren’t as big or as strong as the initial ripple, but they essentially mimic the original ripple.

Molecules move within a structure, if they are pushed a little bit they will move to one side and then fall back towards their original position. Now depending on the molecular structure how quickly they fall back changes, if a second push comes along just as they are returning to their original position it can act like someone on a swing so the molecule moves further the second time. If these pushes continue to match the molecule swing they are making the molecule resonate.

A resonant frequency is just the frequency that something naturally oscillates at.
Think of people rocking a van side to side; it wants to rock at a certain rate with the suspension squeeking. That rate is it’s resonant frequency.
Another example, you’re holding a slinky spring and it’s bobbing up and down. That rate is its resonant frequency.

These things have easily observable resonant frequencies, but everything has one and most are too fast to see. Next think of a wine glass half full that you flick. It makes a distinct note whenever you flick it. That sound is the structure vibrating and the pitch is the resonant frequency.

Take a look at this bridge disaster for an example of a resonant frequency for a large object:

* Imagine a giant Jello mold.
* Slap that sucker as hard as you can and then watch it in slow-motion.
* You’ll see the force of the slap work its way from one of the mold to the other where the jello would bulge out at the end and then work its way back again.
* In fact you’ll see that slap going back and forth over and over again.
* Each time if passes through, however, it loses some energy.
* Eventually it will totally die out.
* Also important to note, the speed with which that slap makes its way through the Jello has nothing to do with how hard you slapped it, but rather the physical properties of the jello.
* Now imagine you could slap it really fast, faster than the slap moves through the jello.
* Again watch it in slow-motion and you’ll see that now there are many slaps working their way forward and then backward in the jello.
* What happens if you happen to slap it right at the same moment that a previous slap was about to make another loop?
* You’d get a super slap because you have the energy of the previous slap plus the new energy you added with your own slap.
* The Jello would bulge out extra far.
* Remember the speed at which the slaps move is based entirely on the jello.
* So as you can see if you slap the jello at just the right speed you can always get the slaps to line up and cause a super slap.
* This is resonance.
* It’s when the natural speed of vibration of an object lines up with the speed of some external source of vibration.