3D - 2

Is there a 3d model of a sound wave?

I was watching fire works, and I thought about the sound wave coming from the explosion, and I was wondering because we know sound travels in a wave, so is there like a spherical model of sound coming from an explosion of some sort.

Public Comments

1. Yes, there are 3D descriptions of sound waves and light waves and most other sorts of waves. The general solution to wave problems in 3D, especially in spherically symmetric systems, involve spherical harmonics. If you are familiar with the solutions to a vibrating string, then you know that there are multiple solutions, each with a integer number of half wavelengths fitting onto the string. That actual solution will be some combination of all or some of these solutions, added together in superposition. Well, if you solve for a wave in 3D instead of that 1D string problem, you get a similar situation, where each of the spherical harmonics (which are a mathematical function that you can look up if you are interested) is one of the solutions and the total solution will be some sum of these spherical harmonics. The spherical harmonics dictate the angular distribution of the sound wave and then there will be a radial term that dictates how the sound wave dies off with distance from the source. This general idea is applicable to practically all spherical problems be they sound waves or radio waves or atoms or anything else spherical. There will always be a spherical harmonic that dictates what the angular dependence is and a radial term that dictates the radial dependence.