# Relationship between amplitude and loudness (again)?

I feel that this type of question has probably been asked a zillion times before, but after reading the basics of audio and sound there is still something basic that I'm unsure of...

Consider a pure tone (single-frequency) sound wave for simplicity. I understand that perceived loudness is correlated (in a somewhat complicated way) with the amplitude of such a wave. But "amplitude" is sometimes used ambiguously... Is it the actual value of the sine function through time, or the peak amplitude that determines loudness?

For example, a sinusoid will have exactly one peak-amplitude, but the value of the sine function might oscillate between two extremes (1 and -1, for example). Is the sound "actually" getting louder and quieter in a way that is imperceptible to us, or is it constant because it's the single peak-amplitude that determines loudness?

Amplitude is an objective measurement. In a waveform, it is the value of the y axis at any given point in time.

Loudness is a subjective measurement, based on how we perceive amplitude and other psychoacoustic dynamics like the Fletcher–Munson curves.

There is no absolute way to measure loudness, there are many different options that will give you different results.

Is it the actual value of the sine function through time, or the peak amplitude that determines loudness?

Both. The sine function through time is what you are measuring, so you definitely need it for measurements. Amplitude is one of the dynamics you need to determine loudness, so you'll be using the peak amplitude of the portion you are measuring too. It might be the case that the part with most peak amplitude is not the loudest, but you are still using that peak amplitude (and any other amplitude value) to determine the loudness of that segment.

For example, a sinusoid will have exactly one peak-amplitude, but the value of the sine function might oscillate between two extremes (1 and -1, for example). Is the sound "actually" getting louder and quieter in a way that is imperceptible to us

Yes. That amplitude oscillation is what we perceive as sound.

or is it constant because it's the single peak-amplitude that determines loudness?

It is constant because there's no difference between cycles. Every cycle is identical.

• Thanks. I have a follow up question about how this generalizes to more complicated audio. Considering an audio signal with a wider frequency band (maybe representing a music track): given what you say, is it therefore true that lower amplitude points on this signal do not necessarily mean that the audio gets quieter at those points? (Maybe because all of the component sinusoids that add up to produce that signal just happen to "dip" at that point, even though they all have a high peak amplitude?) My apologies if this follow up question is not clear...
– user15226
Aug 24, 2015 at 20:40
• @Adam It does get quieter, but you might not perceive it. When the oscillation happens around 20 times per second or faster we start perceiving it as sound. It feels like you are trying to understand more complex subjects without knowing the basics. You might feel more comfortable if you study the basics first, and then revisit the loudness concept in the future. Your questions should be clearly answered once you visit the basics. Aug 24, 2015 at 21:21
• Thanks again. And fair enough. I guess I was thinking that loudness is a basic concept :P
– user15226
Aug 25, 2015 at 12:19
• @Adam It is a basic concept, but you need to have an understanding of the more basic stuff to fully get it. Aug 25, 2015 at 15:51