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General equation for the speed of sound? 
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#1
Feb512, 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 casesgasses, 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? 


#2
Feb2212, 10:50 AM

P: 8

c = [itex]\sqrt{P/\rho}[/itex]
Where P = coefficient of "stiffness" and [itex]\rho[/itex] = density 


#3
Feb2212, 10:51 AM

P: 8

oops sorry. Didn't understand your initial question. I just jumped to conclusions.



#4
Jan1413, 10:39 AM

P: 218

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... Anyone? 


#5
Jan1413, 12:39 PM

P: 218




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