What should I read to understand the math behind waves?

Question

I'm learning differential equations and waves - following online courses and reading some textbooks - and I find that quite often, the use of Phasors, equations combining sinusoidal waves of different amplitudes and frequencies (the derivation of beats)...etc...they're explained really briefly, without a lot of diving deeper into them, and then applied.

Is there a specific "math" which I could study, or textbook I could read, that presents these subjects more explicitly? The more geometric and intuitive the math book is, the better! I tried looking for "wave mathematics" but...found mostly really advanced books. Complex Analysis didn't seem to fit either...

All and any recommendations are welcome, thank you so much!

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Edit:

Books on the differential equations of waves are helpful...but, I think I'd like to start simpler.

What led me to asking this question is that it took me a long time to understand the geometric intuition for how to combine waves of the same amplitude but different frequencies (for which this - https://www.jstor.org/stable/27965328?seq=1 - helped quite a bit) and I still don't understand at all how to combine them if they have different amplitudes!

Is there not anything simpler than a differential equations approach, or pherhaps a book that DOES go into the differential equations, but also does so explaining each step, instead of skipping over the "basic" math of waves?

Thanks again.

Answer 1

Perceptions of what constitutes "really advanced books" is rather subjective. If you're looking for texts that go as far as covering the differential equations of wave motion, I doubt if you're likely to find anything more elementary than the following:

• A.P. French, Vibrations and Waves, W. W. Norton & Company (1971);
• C.A. Coulson, Waves, 2nd edition, Addison-Wesley Longman Ltd (1977).