## Help visualizing and understanding tangential standing waves

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### Help visualizing and understanding tangential standing waves

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?

obieJon

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Joined: Fri Apr 07, 2017 5:20 pm

### Re: Help visualizing and understanding tangential standing w

You need symmetry.
If you shift the parallelogram you violate symmetry.
A standing wave is not a scalar but a vector creating a fixed, symmetric pattern in a room.

Antinodes are always in the corner, pressure flows to boundaries.

"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."
I'm not sure I understand your question.
If you view life with the knowledge that there are no problems, only opportunities, you are a marketing manager.......this is my personal philosophy
bert stoltenborg

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### Re: Help visualizing and understanding tangential standing w

To expand a little on what Bert said about symmetry: because the angle of the reflected sound wave has to be equal with the angle of the incident wave, you will practically find only one solution for the parallelogram in that particular rectangle, which is a rhomboid (all sides of equal length), with its corners in the centers of the rectangle's sides.
... studiOTipper ...
J.F.Oros

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### Re: Help visualizing and understanding tangential standing w

Flav,

Everything OK? We need to go OT, of course.
If you view life with the knowledge that there are no problems, only opportunities, you are a marketing manager.......this is my personal philosophy
bert stoltenborg

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Joined: Sun Apr 18, 2004 11:03 am
Location: Achterhood, Netherlands

### Re: Help visualizing and understanding tangential standing w

Ok Bert, lets do this! The thread starter doesn't seem to care much about people replying to him anyway
... studiOTipper ...
J.F.Oros

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Location: Romania

### Re: Help visualizing and understanding tangential standing w

We're so awesome in explaining tech stuff that no questions remain
If you view life with the knowledge that there are no problems, only opportunities, you are a marketing manager.......this is my personal philosophy
bert stoltenborg

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Joined: Sun Apr 18, 2004 11:03 am
Location: Achterhood, Netherlands

### Re: Help visualizing and understanding tangential standing w

Couldn't one fill the room with different gasses ?

That should open up the room for OT responses
Yannick

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