Register to reply 
General equation for the speed of sound? 
Share this thread: 
#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: 215

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: 215




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 