Making waves – the physics of sound

One of the reasons I got interested in physics as a kid – and still am today – is because of the way sound works. In physics terms, sound is simply a succession of alternate compressions and rarefications of the air, carrying energy which moves our eardrums.

Hammond Novachord. Larry Hammond’s polyphonic synthesiser… from 1938! How awesome is that? Public domain, via Wikipedia.

What does that mean? The first point is that volume is a direct product of the amount of energy in the wave. That same energy, at appropriate frequencies, also causes suitable objects to resonate – hence the trick where a singer shatters a wine-glass, even though the total energy in the wave can’t break the glass. But when the frequency of the note hits the resonant frequency of the glass and compounds the oscillations – yes it can. You don’t have to be an opera singer to do that, but you do have to hit the right frequency by ‘gliding’ the pitch upwards until you see the glass oscillate – it’s to do with resonant frequency, not volume.

That also counts me out. I did actually sing on stage once in student musical after I’d re-written the piece to match what I could do – which, really, means my singing voice has a range of about three semitones. An experiment not to be repeated. Hey – some people have actual ability in the singing department. I am not among them.

For me, though, glass-breaking is only the start of the awesome with sound and physics. Get this: the frequency of a sound wave refers to the pitch you hear, and if you know the frequency you can figure out either the wavelength or the speed of that sound, providing you also know the air temperature and pressure. Just to wrap a bit of math around that, the naked frequency calculation is f = v/λ, where f = frequency in cycles per second (hertz), v = the speed of sound (in metres per second) and λ is the wavelength (in metres). However, the speed of sound varies depending on air temperature and pressure, so you also need that data in order to get a precise measurement. On the other hand, if you know the frequency, wavelength and air pressure, you can deduce the temperature (or, conversely, deduce the air pressure if you know all the other factors).

Why does this matter? In everyday life, it doesn’t, particularly; but there is a lot more to the physics of sound than this. One of the coolest things about the physics of sound propagation is that you have to be some proportion of a wavelength away – and ideally half – to hear a note properly, because the energy maxes at the peak of the wavelength. But because different notes have different frequencies, hence wavelength, it means that bass notes are audible (because of the delivered energy) from far further away than higher pitches. You know those idiots who drive through suburban streets with burping sub-woofer, rattling windows? The driver can’t properly hear those notes, they’re too close to the speaker, and one of the reasons they crank that volume up (apart from this behaviour being the modern-tech equivalent of gorilla chest-thumping) is that this eventually makes the bass audible along with the  treble. Alas, because lower-frequency sounds also penetrate distance further, as another function of wavelength and net energy, you don’t hear the top end they’re listening to. You just get the irritating bit.

Where this gets interesting – for me, anyway – is in the shape of those sound waves.  Different wave-shapes have different sounds – ‘timbre’.

How a sine wave can be plotted by applying the SINE function to a circle, via

The purest tone is a curved wave in a smooth cycle. This is known as a sine, because if you plot it on a piece of paper it’s a trigonometrical solution (remember sines, cosines and tangents?). Whether it keeps its smoothness after going through an amplifier and speaker is another matter, which is why I never built a Mystery Puke Induction Device. There’s no such thing as a ‘brown note’ that causes you to suddenly lose bowel control. But sub-sonics will make you nauseated – especially if you’re up to half a wavelength away. The effect’s been well known for decades. I wanted to use a pure sine in my mad scientist creation because it’s inaudible subsonically, but I couldn’t figure a way of avoiding even miniscule distortion via the amplifier and speaker – stopping it being a sine and creating harmonics that certainly would be audible (for various reasons, apart from anything else, if a tone has an audible-frequency second harmonic then the base tone becomes audible even if it’s at sub-audible frequencies, not that boy racers with a car full of speakers realise the point, because the harmonics disappear faster than the primary tone due to the energies involved.)

What does a sine sound like? No acoustic instrument can produce a perfect sine – the nearest is probably a flute. Even then it’s more triangle than sine, and the ‘breathy’ sound adds textures a sine doesn’t have. Especially if you’re Ian Anderson.

Me practising the Carlos Santana Secret Chord Progression on my Roland Alpha-Juno 2.

Three main factors go into creating the wave-forms that acoustic musical instruments produce; the basic frequency (fundamental or ‘first harmonic’) – which gives the basic pitch; and harmonics or ‘partials’ – which are higher-frequency waves that occur simultaneously with the base wave. These are measured as multiples or fractions of the fundamental frequency and combine to create the specific wave-form.  All these harmonics, including the first, can also have sub-harmonics of themselves, which play an important part in the timbre even if they are below audibility, because sub-harmonics have their own harmonics that are audible. To my mind, for great sounding timbre you can’t go past the lower register of a piano – which produces a very complex wave-form, largely on the back of the fact that the lower notes have three strings that go slightly out of tune with each other and produce ‘beat’ notes or ‘growl’ on top of the wave-form, which are the waves each string produces interfering with each other.

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There’s a lot more I could say about sound. And the same physics, incidentally, apply to any wave in any medium – including rock. Yeah, I’m thinking earthquakes and the energy they deliver. Another time. Meanwhile, for scienc-y stuff of a different kind, check out my book Explaining Our Weird Universe. You know you want to.

Copyright © Matthew Wright 2018