Question

The speed of sound in a medium depends on:
A. The elastic property but not the inertia property
B. The inertia property but not the elastic property
C. The elastic property as well as the inertia property
D. Neither the elastic property nor the inertia property.

Answer 1

Hint: The speed of a longitudinal wave depends on the inertial and elastic properties of a medium.

Complete step by step solution:
In longitudinal waves, the constituents of the medium oscillate along the direction of wave propagation. The speed of a longitudinal wave depends on inertial property as well as elastic property of the medium.
The longitudinal waves, such as sound, travel in the form of compressions and rarefactions. Therefore, bulk modulus of the medium B can be associated with the elastic property of the medium.
Further inertial property relevant for the propagation of these waves is the mass density (\[\rho \]), of the medium.
In general the speed of longitudinal waves in a medium is
\[v=\sqrt{\dfrac{B}{\rho }}\]
Where, B is the bulk modulus of the medium and \[\rho \] is the mass density of the medium.
So, speed of sound depends on inertial property as well as elastic property of the medium.

Therefore, option C is the correct answer.

Additional information:
The speed of sound is greater in solids and liquids than in gases even though they are denser than gases. This happens because they are much more difficult to compress than gases and so have much higher values of bulk modulus. This factor compensates for their higher densities than gases. A sound wave travels faster in a medium having low mass density.

Note: For the propagation of a mechanical wave, a medium is essential having properties of elasticity and inertia. The speed of sound in gases is also affected by temperature, pressure, humidity and molecular weight.