First, let us learn what is sound.
A sound is a longitudinal wave means the medium that the wave travels or moves back and forth in the same direction that the wave is moving.
But the string instruments create sound when their strings vibrate in the air. These instruments use a special wave called standing waves.
What is Standing Wave?
A standing wave is a wave that looks like it is not moving, its amplitude may change, but it is not travelling anywhere. This happens because of reflection and interference.
Reflection occurs when a wave pulse down a fixed rope until it reaches the fixed end and then moves back along the same path. If we send a continuous wave down the rope, then interference takes place.
The wave reaches the end of the rope and gets reflected, but as more peaks pass each other, they interfere with one another, changing their sizes.
In certain frequencies, the reflected waves interfere in such a way that you end up with a way that seems to stay perfectly still, with only its amplitude changing, and there occurs a standing wave.
Different Frequencies Corresponds To Different Musical Notes
The Standing waves can happen both in strings in string instruments and in the air in pipes/flute that makes music. Standing waves with different frequencies correspond to different musical notes.
To understand this, let us know the depth of physics behind the standing wave concept. The points of a standing wave at the maximum height of the peaks are antinodes. The points that do not oscillate or zero peaks are nodes.
On a String Instrument:
You can see where the nodes and antinodes are if the strings create a sound wave. The standing wave creates either peak along the string between those peaks or standstill. If one or both of the strings’ ends get fixed, then each fixed end is a note.
On a Wind Instrument:
Like pipe/flute, the standing waves formed of air molecules moving back and forth mostly near any open ends of the pipe, form the peaks and make antinodes. Between those peaks, at any closed ends of the pipe molecules don’t move at all. Those are the nodes.
All these standing waves give rise to the concept called harmonics.
What is Harmonics?
Musicians make their music using the frequencies of the standing waves. But the nature of these waves depends on the ends of the string. A fixed end will invert the wave turning crests into troughs and vice versa, while a loose end just reflects it without inverting it.
The same thing holds true for air in a pipe/flute. A closed-end will invert the wave, while an open-end won’t. The properties of a standing wave depend on a string with two fixed ends, or a pipe with two ends open, or a string or a pipe with one end fixed, and the other open.
A string with two fixed ends like in a piano that the wave made by a fixed string will have at least two nodes - one at each end and one antinode in the middle, like some kind of one-dimensional jump rope.
The set of all standing waves, known as the harmonics of a system. The simplest or the most basic kind of standing wave of the harmonics called the fundamental or first harmonic. The subsequent standing waves called the second harmonic, third harmonic, etc are the overtones.
Subsequent Standing Waves
The fundamental or the 1st harmonic is the simplest standing wave with the fewest nodes and antinodes. Complex standing waves are overtones. Overtones build on the 1st harmonic increasingly, each overtone adds a node and an antinode. So each of these overtones gets related to the fundamental wave, and all the overtones related to each other.
Together the fundamental wave and the overtones make up harmonics. The fundamental is the 1st harmonic and the overtones are higher-numbered harmonics. With each node and antinode pair that’s added to the standing wave, the number of the harmonic goes up to the 2nd, 3rd harmonic and so on.
Stay tuned till next Friday to read the continuation!
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September 25, 2020
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