3.6.24. The compressibility of mercury, water, and air are $3\times10^{-5}$,$5\times10^{-5}$, and $0.71$ atm$^{-1}$, and their densities are $13.6\times10^3$,$1\times10^3$, and $1.2$ kg/m$^3$, respectively. Determine the speed of sound in these media.
Solution
The speed of sound is $v=\sqrt{K/\rho}$, where $K$ and $\rho$ are the bulk modulus and the density of the medium, respectively. The bulk modulus is the reciprocal of the compressibility of the medium. Using $1$ atm $\approx10^5$ Pa, we obtain the bulk moduli of mercury, water, and air as $3.3\times10^9$,$2.0\times10^9$, and $1.4\times10^5$ Pa, respectively. Thus, the speeds of sound in these media are roughly $500$,$1400$, and $340$ m/s, respectively.