Resonance In Musical Instruments
![[url=https://remote.rsccd.edu/en/band-music-musical-instruments-691224/,DanaInfo=pixabay.com,SSL+]"Saxophone"[/url] by Free-Photos is in the [url=https://remote.rsccd.edu/publicdomain/zero/1.0/,DanaInfo=creativecommons.org+]Public Domain, CC0[/url]](https://www.geogebra.org/resource/k9Z4VWuu/njti1yMl5p7w3Aiv/material-k9Z4VWuu.png)
In musical instruments the idea is for the mass of air and/or the body of the instrument - whether it be a trumpet or a piano or a guitar - to resonate at frequencies corresponding to the musical pitches that we like to hear as musical tones or notes. The size of the cavity, among other things, plays directly into the primary resonant frequencies of an object. For low frequencies to resonate, we need long wavelengths to exist inside the cavity, and thus the cavity must be larger. That's why a cello is larger than a violin, and a tuba larger than a saxophone. So the range of sounds able to be played on an instrument determines its size.
The complex shape of the body of a guitar, for instance, is due to the fact that the guitar plays sounds corresponding to a variety of wavelengths. Imagine you wish to create a resonance chamber that has paths for sound to bounce inside of a variety of different lengths. What shape would you choose? That's the thinking that would have to go into guitar design... along with location of the sound hole and the requirement that it be comfortable enough to hold in your lap.
Resonance and Absorption
I mentioned in an earlier section that objects resonate at frequencies at which they do a good job of absorbing energy. That should certainly sound confusing. If an instrument is meant to emit sound to the environment, shouldn't absorption be the last thing it should do!?
The trouble is that often when energy gets absorbed, it gets lost to forms that are not recoverable. In those cases it's generally converted to heat. That is not what's going on here. Rather, a system like a saxophone will keep absorbing waves of specific frequencies until it is figuratively ready to burst with sound pressure, and it's the overflow of this sound that escapes to the environment. Inside the instrument sound waves bounce back and forth and back and forth always adding constructively to one another such that a relatively large sound pressure is built up as compared to outside ambient air. A little bit of this escapes and makes the sound of the sax.
Try this analogy with a child on a swing: It's easy to make a child swing with very large amplitude if you push at the right frequency. This adds tremendous energy to the child. The child is absorbing your energy. The child swinging wildly actually gives back some of that energy to surrounding air. It's not creating a pitch we can hear, but it still stirs up the air nonetheless. Ask yourself this: If we pushed at a different frequency at which the child didn't absorb your energy effectively, how much would they stir the atmosphere? Not much at all. Do you see the connection to the saxophone? The saxophone is really good at absorbing the frequencies its meant to play, and it stores up great energy at these frequencies. It has so much stored at these frequencies that it is able to give off much to the environment as its very distinct sound.
Energy in Sound
I used words in the last paragraph like "great energy" in referring to the sound energy build up in the saxophone. We should ask this: "Great comparing to what?" The sun? Well, if you are concerned about clean energy you aren't likely to find a solution in sound.
A student of who I am fond due to his endless ideas and enthusiasm came to me one day asking about recovering sound energy near a California freeway. He reasoned that all that sound energy is lost and that collecting it might be a solution to our energy crisis. While such out-of-the-box reasoning is good, the numbers are not. Sound has pitifully little energy in it. In fact, an entire orchestra playing a crescendo (very loudly) just barely makes enough energy to power a single, small light bulb. You could shout non-stop for a whole year about how much you love physics and you wouldn't have produced enough sound energy to make a cup of boiled water for coffee!
Sound pressures are very tiny compared with ambient atmospheric pressure. Atmospheric pressure is measured in pascals, where . The pressure of the atmosphere near sea level is . A sustained sound loud enough to permanently damage your hearing only tends to add (or subtract) 1-10 pascal to that pressure as it oscillates, or changes the atmospheric pressure by around 0.001%-0.01%. While that's not impressive, what is impressive is that we can hear it. What's more impressive about human hearing is that we can hear sounds delivering times less energy than that! The accepted threshold of human hearing is a pressure variation of . That's micro-pascals! The energy delivered by sound of that level is roughly ! We have a marvelous system set up for hearing sounds in our environment. In order to be so sensitive it is also very delicate. In fact, much of it relies on single molecule links within the cochlea. I learned a lot about human hearing from a physics professor with whom I worked as a graduate student because he lost his hearing in his twenties due to a side-effect of an antibiotic. What I learned about human hearing and the signal processing and enhancement that the brain takes the liberty to perform is truly staggering! Remind me to tell the story in class.