Standing Waves on Guitars
Why is it that you press down the guitar string closer to where you pluck when you play a high note? The physics of sound can explain such phenomena.
When you pluck a guitar string, you are essentially inducing what is known as a standing wave on the string. The plucked string is fixed at both ends, while the middle oscillates up and down very quickly, resulting in what looks like a standing oval along the string. Therefore, the term “standing wave” is aptly and intuitively named. In this particular case where the standing wave looks like one oval (not two or three, etc.), the wavelength of the standing wave is simply twice the length of the “oval.”
Standing waves on guitar strings look sort of like single ovals.
To understand how you can get different tones of sound from one guitar string, we need to understand how sound and wavelength of the standing wave are related. One basic relation in mechanics is that speed equals the product of wavelength and frequency. We can apply that to sound: the speed of sound equals the wavelength times the frequency of oscillations of the vibrating object. The vibrating object in this case is the plucked guitar string. We can assume that the speed of sound in air is constant (the speed of sound is different in other media, such as water), so essentially the wavelength and frequency of the standing waves are inversely proportional – a short wavelength leads to a high frequency, and vice versa.
Now, where does the actual sound that we hear come in? The induced frequency from the standing wave’s wavelength gives rise to the sound that we hear. As long as there is an active wave on the guitar string (meaning the string is moving due to plucking and not just sitting there doing nothing), there is an associated wavelength and therefore a frequency as well. High-pitched sounds have high frequencies, and low-pitched sounds have low frequencies. Therefore, to get a high-pitched high-frequency sound from a guitar string, you want to fix one end of the string with your finger so that the wavelength is short, and this happens to be the part of the fingerboard closest to where your plucking fingers are. Using the same logic, you can get a variety of pitches by fixing the string’s end at various locations while plucking, which is exactly what guitar players do.
This is how you get different pitches of sound from one guitar string. There are other interesting aspects of musical instrument design, such as why different guitar strings have different pitches themselves, and how wind instruments (such as flutes) work.
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