Hi!

I understand how to calculate the frequencies of tangential standing waves using Rayleigh's equation but i'm confused about just about everything else on the topic.

In most textbooks the tangential standing wave is visualized as a ray tracing around a 2d space, hitting each wall once (in the case of 1 1 0 ). I'm not very strong in geometry, but isn't there an infinite amount of parallelograms you can fit into a rectangle? So how is there only a single 1 1 0? I understand that the sides of the parallelogram within the rectangle have to be integer multiples of each other... but surely there can be more than just one that satisfies the math.

And how does the fact that pressure maxima are always in the corners have to do with the ray tracing around (and never touching the corners).

I'm also confused by how the length/width of the sides of the standing wave parallelogram relate to the length/width of the sides of the room. In Rayleigh's equation we seem to be only plugging in numbers related to the room dimensions.

Anyone have a good animation of a tangential standing wave they can share?

Thanks for your time!