Question

Sound travels fastest in which of the following substances:
(A). solids
(B). liquids
(C). gases
(D). none of these

Answer 1

Hint: The speed of the sound depends on the density of the medium through which it is traveling.

Complete step-by-step solution -

Sound waves travel through a medium by longitudinal propagation. It means there are alternate contraction and expansion of particles in the medium. Its propagation mainly depends upon the density of the medium.
As the propagation of sound can be considered as the propagation of disturbance in the medium. If we consider the case of solids, the density will be more for solids as compared to the gases. If the density is more, then the collisions will be more. Due to the close arrangement of molecules, the collisions take place very quickly, and thus the sound wave travels at a higher speed.
The correct answer is option A i.e. Solids.

Additional Information:
We should also talk about the dependence of the speed of sound on the density of the medium in the case of gases. Because students usually try to use the same formula for solids that have been used to find the speed of sound in gases. So, the formula governing the speed of sound in gases would be:
$v=\sqrt{\dfrac{\gamma P}{\rho }}$
Here $v$ is the speed of sound,$\gamma $ is the coefficient of adiabatic expansion, $P$ is the pressure of the gas, and $\rho $ is the density of the gas.
Here the density is inversely proportional to speed. In the case of gases, the speed of sound decreases with an increase in density.
For solids we have to use the equation with Young’s modulus.
\[v=\sqrt{\dfrac{Y}{\rho }}\], where \[Y\] is the Young’s modulus and \[\rho \] is the density of the material. Here also density is inversely proportional to the velocity of sound. But, in the case of solids, the elasticity will compensate for the effect of density. That’s why the speed of sound is more in solids than gases, even though they have large density. We can remember that steel possesses more elasticity than rubber.

Note: Do not apply the formula of the speed of sound in gases for the case of solids. Because this formula is derived by considering the motion of gas particles in a container and the gases have more degree of freedom as compared to that of solid particles.