Updated: Aug 5
Our Chief Assessor, Toby, describes an awesome lesson delivered by a prospective tutor, in which he was taught how equations can explain the way guitars are played.
In Kinsgley Amis’s thoroughly researched book on the effects and pleasures of consuming alcohol, Everyday Drinking, he is rather scathing about scientists. “Alcohol science,” he remarks, “is full of c**p. It will tell you, for instance, that drink does not really warm you up, it only makes you feel warm--oh, I see [...] In the same style, the said science will maintain that alcohol will not really fatten you up, it only sets in train a process at the end of which you weigh more.”
I sympathise with Amis. I was never much of a Science student at school, and I often felt reluctant to accept the counter-intuitive assertions my Physics teachers made, such as “kilograms are not a measurement of weight, they are a measurement of mass,” or that when you look at a wave crashing down onto a Californian beach “it is energy, not water, that is being transferred through space.” All I can say is it jolly well looks like the water is being transferred through space.
For this reason, when I encounter a Science teacher who is able to reach through my fog of misconceptions, and bring me to better understanding, it’s a delightful thing. A great example was the interview candidate who taught me about the Physics of a guitar string.
It was a terrific lesson choice. As she knew from reading my profile, I am enthusiastic (although rather poor) guitar player. It is always a good idea for a teacher to try to relate the content of their lessons to something the student is already interested in, and the Physics teacher in question did this to a tee.
As any guitar player knows, there are a few things you can do to change the pitch of a given string. You can tighten or loosen the string via the tuning peg. You can push down with the fingers of your left hand to cut the string off at a particular fret, thus shortening the string. And once you have fretted the string, you can bend it with your left hand to raise the note either a half or full step, or perhaps colour it with a little vibrato.
The question is, how does a physicist’s understanding of waves explain what is really going on? The first thing to establish is that a plucked guitar string forms what’s called a standing wave. This means that some parts of the string remain static while other parts vibrate with maximum amplitude. If you film a guitar string vibrating in slow motion, you can see how it resembles a Sine wave. (For the curious, YouTube is full of such videos.)
Right, now that we know what kind of wave a guitar string makes and what it looks like, we can consider the properties of such a wave. Physicist tell you that waves can be measured in three different ways.
• First, there’s the Amplitude. This is the vertical distance between the medium of a wave and its peak. Or, put another way, this is half the distance between a peak of a wave and a trough. In terms of sound waves, amplitude represents volume. This means if you hit the strings harder, the waves they form have higher peaks and lower crests, and the sound produced is louder.
• Next, there’s the Wavelength. This is the length of one complete wave, or the horizontal distance between two peaks. The wavelength, unlike amplitude, does not in of itself relate to the sound the guitar produces. But it is inversely proportional to…
• Frequency. The frequency of a wave is the number of times a point on a wave passes a fixed reference point in one second. In terms of sound, frequency is related to pitch. A higher frequency (more waves per second) gives us a higher pitched note; a lower frequency (fewer waves per second) gives us a lower note. As I mentioned, frequency is inversely proportional to wavelength. (For non-mathematicians, this means that one quantity increases as the other decreases, or if you double the frequency, the wavelength halves.) By fretting a string you shorten it, which reduces the wavelength. This in turn causes the frequency to go up, and so the pitch of the note produced rises.
The relationship between frequency and wavelength, expressed mathematically looks something like this:
f = k/λ
(where f is frequency, λ is wavelength, and k is a constant.)
The constant, k, is affected by a few things, including the material the string is made out of, it’s thickness, and the tension in the string. This is why thicker guitar strings produce a lower note than thinner ones, and why tightening or loosening the tuning peg (which changes the tension in the string) also impacts the pitch of the note. Bending the note, like turning the peg, exerts a small change to the tension, enabling the player to sculpt the note as they choose.
What I so admired about this lesson, is that the tutor took what might otherwise have been boring material (the properties of a wave) and made it interesting to me. If you can do that, the battle is virtually won already.
Blog Post Crafted by Toby
Toby is in charge of recruitment of new tutors. He conducts interviews with prospective tutors and assesses their lessons to get a feel for whether they have the teaching style we're looking for.