Volume: How Big the Wave Is

The last machine played a tone. But how loud was it? What controls that? When a speaker pushes air, it can push gently or hard. How far the air molecules actually get shoved is called amplitude, and it's what your brain perceives as volume.

Drag the volume slider while it's playing and watch the oscilloscope. The wave gets taller when you turn it up and shorter when you turn it down. Same frequency, same shape - just bigger or smaller swings. That's amplitude: the height of the wave from the centre line to the peak.

Now look at the number next to the volume slider. It says something like -7.5 dB. That unit - the decibel - is one of the most beautifully deranged units in all of science.

Decibels are logarithmic. Every increase of 10 dB means the sound energy has multiplied by 10. Every 20 dB means the energy has multiplied by 100. This seems like a terrible way to measure something until you learn why it exists: your ears are logarithmic too.

The quietest sound a healthy human ear can detect is about 0 dB SPL - roughly 20 micropascals of pressure. A jet engine at close range is about 140 dB SPL. The difference in actual energy between these two is a factor of 100,000,000,000,000. One hundred trillion. Your ears handle this entire absurd range and make it feel like a smooth gradient from "quiet" to "loud." That's a biological engineering decision of staggering ambition.

The slider uses a cubic curve: the gain equals the slider position cubed (after normalising to 0-1). This means the bottom of the slider has very fine control over quiet volumes, while the top of the slider covers the loud end more coarsely. This matches how your ears work - small changes at low volumes are more perceptible than small changes at high volumes. A linear slider would feel wrong: the first 10% would seem to do nothing, then it'd get loud too fast.

Amplitude is independent from how fast the wave vibrates. You can have a high-pitched quiet sound or a low-pitched loud sound or any combination. Think of it as two separate dimensions of the same wave - speed is horizontal (how fast it repeats) and amplitude is vertical (how tall it gets). Two knobs. Two completely separate aspects of what your ear receives.

You now understand the two most fundamental properties of any sound wave. Everything else - waveforms, filters, modulation, effects - is just increasingly creative ways to manipulate these two numbers over time.