The Culprit wrote: ↑Thu Jul 15, 2021 9:03 pm
My first issue is the requirement of a good knowledge of complex numbers. After an hour or so on YouTube I've come to realise that I must not have been in that day at school 20-odd years ago

If you've got some spare time you could learn complex numbers and how they apply to waves. If you learn this you will have a good understanding of phase. At the very least this will mean you can have a laugh at some of the questions about phase, like "How do I get the bass in phase with the drums"

If complex numbers were covered at your school it would be the arithmetic and algebra of complex numbers, which is a necessary background, but it's not obvious how that relates to waves. That's more advanced and is in this equation :

A complex number can represent a sinusoid, and when doing this the vector in the complex plane is called a phasor :

By Gonfer at English Wikipedia, CC BY-SA 3.0,
https://commons.wikimedia.org/w/index.p ... d=11313700
Learning how complex numbers relate to waves would be relevant to acoustics because you can use the e^i*theta notation for sound waves. Phase angle now makes sense because it's the angle between phasors as can be seen here with three phasors producing three sinusoids with different amplitudes and phases :

By Gonfer - en wikipedia, CC BY-SA 3.0,
https://commons.wikimedia.org/w/index.php?curid=7026837
Learn this and be forever entertained by the endless questions about phase.
