General equation for the speed of sound?

by fhqwgads2005
Tags: equation, general, sound, speed, state
fhqwgads2005 is offline
Feb5-12, 02:13 PM
P: 23
I've seen stated in many a physics book that the general case for the speed of sound (for general equations of state p(ρ) ) is given by

[tex] c^2 = \frac{\partial p}{\partial \rho} [/tex]

where p is pressure and ρ is density.

but I can't for the life of me figure out how on earth to derive that. I've seen tons of derivations for specific cases--gasses, solids, but not for the general case. According to wikipedia, it can be derived using classical mechanics. Can someone point me in the right direction?
Phys.Org News Partner Physics news on
Physicists design quantum switches which can be activated by single photons
'Dressed' laser aimed at clouds may be key to inducing rain, lightning
Higher-order nonlinear optical processes observed using the SACLA X-ray free-electron laser
IsaacOh is offline
Feb22-12, 10:50 AM
P: 8
c = [itex]\sqrt{P/\rho}[/itex]

Where P = coefficient of "stiffness"
and [itex]\rho[/itex] = density
IsaacOh is offline
Feb22-12, 10:51 AM
P: 8
oops sorry. Didn't understand your initial question. I just jumped to conclusions.

Sunfire is offline
Jan14-13, 10:39 AM
P: 177

General equation for the speed of sound?

the equation of state is p=p(ρ,s) thus

dp = ([itex]\frac{∂p}{∂\rho}[/itex][itex])_{s}[/itex]d[itex]\rho[/itex] + ([itex]\frac{∂p}{∂s}[/itex])[itex]_{\rho}[/itex] ds

I am guessing that because ([itex]\frac{∂p}{∂\rho}[/itex][itex])_{s}[/itex] has units of "velocity squared", it is looked upon as such;
But why this velocity is the sonic one - beats me...

Sunfire is offline
Jan14-13, 12:39 PM
P: 177
This gives probably enough of an explanation

Register to reply

Related Discussions
Speed of Sound - General Formula General Physics 4
Speed of Sound Lab (using slope to find speed of sound) Introductory Physics Homework 2
Wavelength of sound waves and speed of sound in air column Introductory Physics Homework 1
Velocity of Sound, speed of rock and return of sound Introductory Physics Homework 1
Speed of sound and sound detection lag between ears Introductory Physics Homework 5