Sound Wave Spatial Structure

The spatial structure of a sound wave is directly connected to my previous post about harmonics. In that post, I looked at the relationship between string length and wave velocity, but a comparison can be drawn between the wavelength of a sound wave and the length of its medium as well. This concept was critical in explaining the foundation of my previous two experiments, but was not something that I have dedicated a blog post to. This graphic does an excellent job of reiterating the harmonics of a sound wave, while also illustrating the relationship between the wavelengths of the harmonics and their relationship to the medium:

(The Physics of Music and Color)

Looking at the relationship between the wavelength and the length of the string (L) we get:

Harmonic Mode	Wavelength in terms of String Length(L)
1st	1/2L
2nd	L
3rd	2/3L
4th	2/4L
5th	2/5L
6th	2/6L

This relationship can be modeled by the same equation given in the previous blogpost:

This relationship relates well because the wave velocity (V) is a constant for a specific medium, and was arbitrarily chosen in the example above based on the graphic.

Works Cited:
1. Gunther, Leon. The Physics of Music and Color. New York, New York: Springer, 2012.