10.9.0 Musical Instruments

A guitar string is a string fixed at both ends. When you pluck a guitar string, it makes a sound of a particular pitch. One single pitch, right?

Nope. Using any free software that analyses the frequency content of a sound, we are presented with evidence that the sound wave produced by a plucked string[1] contains many harmonics. The lowest frequency harmonic, which usually has the largest amplitude among all the harmonics, is called the fundamental note. Our brains register this as the pitch of the sound. And we “hear” the higher frequency harmonics as overtones. The number and relative intensity of the harmonics (called the harmonic content) is one of the primary contributors to the timbre of a sound. The difference in timbre is the reason why notes of the same pitch produced by different musical instruments sound different.

So how is the string able to resonate at so many frequencies at the same time?

When a guitar string is plucked, a triangular pulse is sent running back and forth between the two ends of the string. A triangular pulse is actually made up of sinusoidal waves of a continuous range of frequencies (kind of similar to white light consisting of EM waves of a continuous range of wavelengths). The sinusoidal waves whose frequencies match the resonant frequencies of the string will undergo constructive interference. The sinusoidal waves of the non-resonant frequencies will undergo destructive interference. So the string is acting like a filter. It amplifies its harmonics, but stifles the non-harmonics.

Let’s move on to the flutes. A flute is basically an open pipe. When you blow across the embouchure hole of a flute, you are energizing the pipe with white noise. As you may guess, white noise contains the entire range of sound frequencies[2]. So you are producing sound waves of all frequencies that travel up and down the pipe as they are reflected at both ends of the pipe. Again the pipe acts like a filter. Sounds waves of the resonant frequencies are amplified through resonance. Sound waves of all the other frequencies undergo mostly destructive interference and are not heard.

Demonstration

Frequency Analyzer

Concept Test

2065


[1] Strictly speaking, the sound wave is produced by the sound board, not by the plucked string. The vibration of the string is picked up by the sound board, whose vibration produces the sound wave that we hear.

[2] It is called white noise because it has all the frequencies, similar to white light having all the wavelengths.

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