Identifying centre of rarefaction and compression of a graph in a st graph

Question

We know that for a sound wave traveling to the right, the centre of compression occurs at $s = 0$ and $frac{ds}{dt} > 0$ (take right direction as positve i.e. traveling to the right too!). And centre of rarefaction occurs in $s = 0$ and $frac{ds}{dt} < 0$. I have seen some explanation of this using simulation, I wonder what is the theoretical/mathematical proof for this?

acoustics waves

user45664 · Accepted Answer

s=0 and ds/dt > 0 means that the displacement has been increasing, implying compression since it would normally require a force.
s=0 and ds/dt < 0 means that the displacement has been decreasing, implying decompression since it would normally require reducing the force.
The center of compression/decompression s = 0 is the displacement that would occur with no applied force.

Identifying centre of rarefaction and compression of a graph in a st graph

One Answer

Add your own answers!

Ask a Question