## November 04, 2014

### I'm a little bit stuck - where did I go wrong?

I was asked by a colleague why the amplitude of tangential modes of a ring or cylinder scale as $$cos(m\theta)/m$$.

The answer was given by Rayleigh in his Theory of Sound, which you can read on The Internet Archive. Here's the relevant part:

The relevant solution to the differential equation (1) in Rayleigh for the tangential component has the  $$cos(m\theta)/m$$ behavior.

But, I wasn't able to start with Rayleigh's coordinates and end up with his equation (1).

Here's my work; where did I go wrong?

Unknown said...