dismal_denizen

Consider the work of God; who can make straight what he has made crooked?

- Ecclesiastes 7:13

Human beings are remarkably adept at change, people can improve. Do not believe those who would have you think any differently, regardless of whether they recorded their words in an age-old text or not.

“Frequency” is a very important property of sound, and is perceived by humans as pitch. Notes on a piano are different as a result of their frequencies. But what exactly are we referring to the frequency of? What are these mysterious frequencies?

The time domain

Sound travels as a wave, propagating via the vibration of air particles. This is why in space no one can hear you scream - there are no particles to vibrate! It is reasonably common to see drawings of these sound waves, such as the following:

Because this visualization shows us how the amplitude (loudness) of the sound varies with respect to time, we refer to it as the time domain representation of the audio signal. This representation is quite intuitive, as we can immediately understand how, as time passes, the loudness of a sound will vary. In physical terms this wave describes the way in which air particles will vibrate as the sound passes through them.

The frequency domain

At this stage you should be wondering “how does frequency tie into all of this?”. If you are really ahead of the ball you may even know that frequency is how many times per second something happens - that is, how often it repeats. However, if you look at the time domain representation given earlier, there is no pattern, nothing is repeating! How, then, are we supposed to consider the frequency of it?

Any wave may be constructed by adding together multiple cosine waves.

Woah, what was that? Did you say that? Well I know that a cosine wave looks like this, repeating in the same fashion forever:

Notice how the shaded region repeats three times in one second. This means that the frequency of the of the wave shown is 3 Hz (Hz means “times per second”). According to the earlier statement, any sound can be made up of a whole bunch of stretched variations of the cosine wave shown - by “stretched” I mean that their frequencies and amplitudes can vary. If we take each of these constituent cosine waves and use them to place points on a frequency vs amplitude graph the result is a frequency domain representation of the entire sound wave. This shows us “how much” of each frequency component is present. Hence most sound waves don’t have a single frequency, but have many!

A high-pitched sound will have greater amplitudes at higher frequencies than a low-pitched sound will. Tools such as equalizers can adjust how big the cosine waves in certain frequency ranges are, changing the sound. The frequency domain is very useful for manipulating and analysing sound, even if it takes a little bit of thinking about to arrive at.