How do earphones create sound waves that are longer than the size of earphones themselves?
In: Technology
Sound waves are created from something vibrating and then the waves move out away from that object vibrating. Think of like a water wave. You put a toe in the water and ripples travel out from that point. The wavelength (the length of the wave) is determined by the frequency (rate) of the toe going in and out of the water and how fast the waves goes out from the toe. The width of the toe doesn’t matter for the wavelength.
This is an interesting question, because it is misleading in certain ways, which I’ll explain later.
A “sound wave” is basically a periodic change of air pressure and particle velocity. If you imagine a long tube with a short plug inside that you’d be shoving in an out with a stick, this is what would happen: as long as you shove it down, you’d increase air pressure (and shove air down the tube). As long as you pull it out, the opposite would happen.
As always with devices that produce sound for human ears, the details are rather tricky. To produce the intended result (undistorted playback of music), you’ll have to consider far more than the actual solenoid and membrane that make up a speaker. Due to “Newton’s Axioms” (basically, laws of nature that nobody ever has observed to be violated), every force (which the speaker excerts on air before it) will be counteracted by an equal, but opposed force. This is how “inertia” works, for example. So, when the earplug starts to play a bass note (maybe a low, soft note on an e-bass, for example), it will pull at its “cage”, as it is called, at the parts holding the actual speaker. These will pull at the skin in your ear channel, the skin will pull at your skullbone. When all of this would give way (which it can’t), your question would show why bass notes would sound funny, because in the end, even your inner ear would be pulled and then register another sound being “played”. Which didn’t come in through the eardrum, but through the bones. Obviously, that doesn’t happen.
The ear plug sits “tight enough” so that it’s not a problem for the plug to compress the air inside the ear channel further, even if the wave ran all the way to the eardrum already. This you can even hear: if you unplug a plug slightly, music playing back sounds differently. Technically speaking, it’s a matter of dampening and impedance, and the ear itself is already quite good at this. No wonder, it should catch every bit of acoustic energy running down the ear channel to hear finely.
The physics ELI5 is: it can do it because sound waves are [compression / “longitudinal” waves](https://www.youtube.com/watch?v=kxQj-wPePBU).
In other words – the speaker alternately pushes and pulls air along the direction in which the sound moves. Your ear responds to changes in pressure, and how frequently they arrive. The lower the frequency, the longer the wavelength. So the wavelength basically depends simply on how fast the speaker membrane vibrates – not on its size.
The Audio ELI5 is: almost certainly more complicated. Real audio engineering is complex – I don’t pretend to understand most of it – and there will be any number of other factors involved in the final design. Sound volume depends on how much energy goes into the wave, for example, and that’s related to, e.g., how much air the membrane moves as it vibrates – and a small membrane isn’t going to be able to move as much as a bigger one. So a small speaker vibrating slowly can produce a low note, but it’s also going to be a rather quiet one. But in principle the physics holds: there’s very little stopping a speaker of any size producing a note of any wavelength, beyond its physical ability to vibrate at the required speed.
They don’t.
Every note is made up of the fundamental frequency and several harmonics. The harmonics are higher and can be easily reproduced by the headphones. The fundamental is longer wavelength and often can not be reproduced by the headphones. But here’s the thing: your brain has a “correction circuit” in it. If your brain hears the harmonics but the fundamental is missing, your brain fills the fundamental in.
This can be demonstrated with oscilloscopes. https://youtu.be/0amvhGzeCnQ?t=99
Imagine hanging out the back of a pickup truck with a stick with a paint brush on the end.
You wave the stick back and forth as the truck drives along the road.
Now go back and look at the paint on the road. You’ll see a wave pattern.
If the truck was driven at a constant speed and you waved the stick back and forth at the same speed then there will be the same distance between peaks on the wave pattern.
But if you went back and did it again, truck at the same speed but this time you waved the stick back and forth much slower than the first time, you’ll find there is much more distance between the peaks.
This makes sense because during the time it took you to wave the stick from one side of the truck to the other side and back again, the truck has traveled a longer distance on the road.
Sound works the same way. Sound moves through the air at the same speed no matter the frequency. So high frequency sounds have a shorter wavelength because the sound doesn’t travel as far before it completes a cycle.
Lower frequency sounds have a longer wavelength because they travel farther during a complete cycle.
Notice that none of this had anything to do with the size of the speaker just like the size of the paint brush doesn’t matter only the speed of the truck and how fast you want the stick.
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