Amplitude and Frequency

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Hi there!

My name is Ken Bellows. I'm a software and web developer living somewhere near Baltimore, Maryland, USA. If you care to know more about me, I have a website, though it's perhaps a bit outdated.

This is a tiny little cluster of web pages to host my Peer-Review Assignments for Coursera's Introduction to Music Production course, which I am currently taking. This is my assignment for week 1.

This week's topic is on the Frequency and Amplitude of Sound Waves.

Sound Waves

Sound travels in waves. We all know that. But what you may not know is that a sound wave is not your average wave. (Well, actually, based on sheer prevalence, it's probably fairly average, discounting light waves.)

Usually when we think of a wave, we think of ocean waves and pond ripples, with a nice, even up-and-down sort of motion.:

This is referred to as a transverse wave, and it's how plenty of waves work: water ripples, light waves, seismic waves, hand waves... But this is not how sound waves work.

Sound waves travel in longitudinal waves. In this type of wave, the kinetic enery of the wave vibrates along its length, running parallel to the wave's direction of travel, rather than perpendicular to it, as it would in a transverse wave.

In the case of a sound wave travelling through the air, the wave pushes and pulls the air around itself forward and backward with it, resulting in small pockets of pressurized air and rareified (depressurized) spaces in between them.

These waves of pressurized and rareified air pockets are what our ears understand as sound. Generally speaking, differently organized waves are heard as different sounds. Waves have many different properties that affect how we hear them. Two of the most important and best understood of these properties are Frequency and Amplitude.


Frequency is the word we use to talk about how "large" these pockets of air are, so to speak, or rather, how frequently they occur. Actually, to be more accurate, the word we use to talk about the size or length of a pocket within a wave, specifically the distance from the beginning of one pocket to the beginning of the next, is period. The period of a wave is actually the inverse of its frequency (1/f). Point being, the longer each packet is (i.e. the larger its period), the less frequently it occurs.

Example: below are two waves. The bottom wave has 4 times the frequency of the first. (As it happens, the two waves have frequencies of approximately 0.5Hz and 2 Hz, respectively; see below for more on the Hertz unit.)

"But wait!" you cry, "What if the packets speed up or slow down? Surely this will affect frequency as well!" Wrong! Well, not actually wrong, because if they did speed up or slow down, that would definitely affect frequency. But remember, the speed of sound is constant within a given medium (air, water, dirt, drywall, chocolate-butterscotch-tapioca pudding). Since this never changes, a stream of air broken into pressurized pockets at a certain regular distance apart will always collide with our eardrum at a steady interval. Our ears use this measurement of how frequently they are being pounded to tell our brains what pitch the sound has. Pitch, then, is essentially our brain's interpretation of the frequency of a sound wave. (There are certain other factors that will affect our perception of pitch, but frequency is far and away the primary factor.)


This one's easier and, I'm sure you'll be glad to know, much shorter.

We've been talking about pressurized air pockets; Amplitude is the word we use to talk about just how pressurized they are. The more powerful the vibrations generating the pressurized air packets, the more pressurized the air packets will become, the more force they will carry with them, and the harder they will hit our ear drums. Amplitude is often equated to how loud a sound is, and, while imperfect, it's not a bad approximation. There are certain other factors that affect how loud our brains think a sound is, such as ambient noise, other nearby sound sources, frequency (those high pitches are always so piercing!), and how high we've turned up our hearing aids, but amplitude is usually the primary factor.

Example: below are two waves. The bottom wave has 3 times the amplitude of the first.

A final note: the usual unit of measurement used to describe the amplitude of a wave is the Decibel (dB). Decibels get a bit tricky, though, because there are two ways to measure them. Remembering that amplitude, and thus decibels, are a measurement of air pressure as a result of sound waves, the first is to measure them in terms of how far above a standard low-end reference number the sound pressure of a wave is. The reference number used is generally the accepted standard lowest level of amplitude a human can hear; this number is assigned 0dB. This is generally how sounds are measured in the field. This type of decibel is often referred to as a dBSPL, where SPL stands for Sound Pressure Level. The other common measurement is how far the amplitude of the wave is below the the highest level a computer or sound system can handle without clipping and causing distortion. These decibels are often referred to as dBFS, where FS stands for Full Scale. In this measurement system, 0dB is the loudest the system can handle without clipping, and all other levels are given negative decibels.


Frequency and Amplitude, while they can each contribute to loudness and (to a lesser degree with amplitude) pitch, are entirely independent beasts. What happened was, they used to be besties, you know, like five billion years back, but then they got in a big fight over who was going to take Timbre to the big dance, and ever since then they haven't been as close. For a while they didn't even talk. Now it's like, they'll work together, you know, for the greater good of the universe and all, but they each pretty much do their own thing after 5pm. It's just not the same any more.

The point is, frequency and amplitude can (and usually do) change entirely independent of each other. Now, this doesn't mean that they don't change simultaneously; this happens all the time. What it means is that they don't have to, and when they do, their values aren't tied together in any way. When the frequency of a wave increases, we can't make any new predictions about its amplitude as a result. It goes the other way, too; we can change amplitude around all day long without frequency ever noticing (or caring, for that matter; and why should frequency care who amplitude hangs out with, anyway? It's just not the same...).


To drive this whole thing home, let's play around a bit with a sound wave. The little mini-demo below will generate a sine wave when the "Start Sound" button is pressed, and stop it when the "Stop Sound" button is pressed. The sound played should match the wave shown and the values displayed below it.

Notice the two gray circles. These are handles: one changes frequency, the other changes amplitude. You can simply play around with the values in silence, turn on the sound and move it around. It's up to you.

Note: You need a pretty new browser for this to work. It's currently tested and working in Mozilla Firefox and Google Chrome, and it should work in Apple Safari as well. All other browsers are entirely untested, and I have no idea whether they will work, though I'd love to find out.

Amplitude: dB
Frequency: Hz


So, to review, we've discussed Sound Waves, Frequency, and Amplitude.

  • Sound waves are longitudinal waves, meaning they oscillate forward and backward rather than up and down.
  • This front-to-back oscillation creates pockets of pressurized and rarified air at a certain frequency, which our ears interpret for our brains as sound at a certain pitch.
  • Similarly, the level of violence with which the source of the sound produces the waves determines the amplitude of the pressurized pockets of air, which in turn heavily influence our perception of the sound's loudness.
  • A system of communication based on a telegraph, a microphone, a large bass drum, and a tennis ball machine firing some assortment of balls, rocks, chickens, and other projectiles is a terrible idea.