The Physics Philes, lesson 112: Sea Shell Resonance
I know last week I said that we’d look at how standing sound waves applied to musical instruments, but as I was preparing I realized that it doesn’t really illuminate anything, so I’m moving on resonance and sound. Sound good to you? Great.
Remember that a normal mode is when all the particles in the oscillating system move sinusoidally with the same frequency. If we can get the oscillation going just right, we get resonance.
Normally, oscillations of a system will naturally die out. However, we can keep a constant-amplitude oscillation going by applying a periodic force called a driving force or a driving frequency. The oscillation that results is called a forced oscillation or a driven oscillation. If we can get the amplitude at the driving frequencies close to the natural frequency, we say we have resonance. Think of pushing a kid on a swing. The more you push, the higher the kid swings. You push periodically with the frequency of the swing and build up amplitude. It’s resonance.
A swing is a system with one normal mode, but, as intimated earlier, we can apply a driving frequency to a system with many normal modes and get resonance, as well. Let’s think about an pipe with one open end next to a loudspeaker that emits a pure sinusoidal sound wave. That loudspeaker provides a driving force, and the air in the pipe will vibrate with that same frequency.
One of three things could happen. If the amplitude of the resulting motion is small, the air inside the pipe won’t move in any of it’s normal mode patterns. If the driving frequency is close to one of the normal mode frequencies, the air in the pipe will move in the normal mode pattern for that frequency. In that case, the amplitude could get large. If the driving frequency is exactly equal to the normal mode frequency, we say the system is in resonance. The amplitude of a system in resonance is at its maximum. If there was no friction, the driving frequency would keep pumping energy into the system and the amplitude would increase forever. But of course in the real world there is always some mechanism that causes energy to leave the system, so this doesn’t happen.
One example of resonance you may have experienced is hearing the ocean in a seashell. The noise you hear is actually the air moving outside the shell. That causes the air inside the shell to oscillate at normal mode frequencies causing the resonance you hear as the ocean. You can also hear resonance when you blow across the top of a bottle of pop. The moving air from your breath causes the air inside the bottle to oscillate in resonance. You can make the sound lower by drinking some of the pop and blowing again. The column of air is longer which translates to a lower sound, much like a longer organ pipe corresponds to a deeper note.
Another example of resonance is breaking a wine glass with your voice. You can figure out the normal mode frequency of the a wine class by flicking it. If you can hit that same frequency and if you can make your voice loud enough, the resonance can break the glass.
Resonance is kind of cool, is it not? Unfortunately, that’s all for now. Next week we’ll start in on wave interference.
Featured image credit: Jason Eppink via Flickr