can every sound be considered as a remix of a sine wave? why?

In: 4

ELI5.

To give you an analogy, think about positive whole numbers, 1,2,3…. It is possible to construct every positive whole number by adding 1’s. So 1 = 1, 2 = 1+1, 3 = 1+1+1…

This is similar to the idea that any sound which, for simplicity, are vibrations can be broken down into sums of a “fundamental” vibrations represented by the sine wave. This is actually not STRICTLY true unless one allows for infinite sums. But for the purposes of analyzing and reproducing sound, ie in the real world of making “stuff”, it is a good enough idea with which to work with and say is “true”. The reason engineers and scientists like to do this is, mathematically speaking, working with sums of sine functions is fairly easy. As long as one is willing to do the computation, by adding more and more sine waves, it is possible to get arbitrarily close to any sound wave.

(The above is pretty hand-wavy. There are pretty specific mathematical and physical requirements that make it possible to make this claim.)

All pure sound waves are sine waves. By “pure” I mean single frequency, eg A-440Hz tuning fork. But no sound in daily life is made up of a single frequency. It is composed of several frequencies all with their own separate sine waves, but your ear hears it all together, all of the sine waves are added up. This summation doesnt even look like a sine wave at all because of all the different amplitudes and frequencies, but with something called a Fourier transform you can decompose this complex wave into all the individual single frequency waves that make it up.

​

Try it yourself. Graph Asin(Bx)+Csin(Dx)+Esin(Fx)…. for like 10 terms. The final wave looks super jagged and doesnt even look periodic at first glance. But its still made up of distinct perfectly periodic sine waves. Same thing happens with real life sound waves.

Sine waves are a mathematical convenience. The equations that come out of sine wave analysis are relatively simple and easy to use. Other wave forms would work, too, but the equations usually get messy quickly. There are some strange artifacts, however, such as the concept of negative frequency. The equations continue to work but the idea is a bit weird. And you often have to deal with infinite series or settle for approximations (when you cut short the infinite terms). The underlying math is best suited for repeating (and infinite) sounds, but the math can be adapted for sounds, light, gravity, tides – any wave forms. In real life, everything is finite or ceases repetition eventually, so those adaptations are important to master. As noted, Fourier analysis is the mathematical basis.

All sound is just vibration, and it’s always in a sine wave. The difference in how a sound sounds is just the distance between waves (period) and it’s height (amplitude).

So all sound is basically the same thing but stretched in two different directions in different amounts for different sounds. Not entirely sure if that categorizes is as a remix, though.