Originally posted by mtthomps
Just another thought. I looked it up. At 25 degrees centigrade the speed of sound in :
Water = 1493 m/s
Mercury=1450 m/s
Pyrex Glass=5640 m/s
Rubber = 1600 m/s
Diamond = 12,000 m/s !!!!
Mercury is over 13 times denser than water. Why is the speed of sound lower in mercury? Pyrex glass, while heavier than water, is not 4 times heavier. Why is the speed of sound in Pyrex Glass that much faster?
The speed of sound in any substance whatsoever is
a = sqrt(B/rho)
where rho is the density, and B is the "bulk modulus". The definition of B is
B = delta(p) / [ delta(vol)/vol ]
or in English (sort of)... B = isentropic change in pressure per fractional change in volume. For isotropic solids, B is proportional to Young's modulus, so that s.o.s. tends to be largest in light and stiff materials. Like diamond, for instance!
From Thermo 101, we know that for an ideal gas
B = gamma*p , gamma = cp/cv
so that
a = sqrt(gamma*p/rho)
and from the Ideal Gas Law we also have
p/rho = R*T
so that finally
a = sqrt(gamma*R*T)
Both gamma and R depend on the molecular type and weight of the gas. For air, gamma = 1.4, and R = 287 J/kg-K, so that
a = sqrt(1.4*287*T) = 20.04 sqrt(T)
Quiz at 11:00 :-)