Question

On what factor does the speed of sound in a medium depend?

Answer 1

Step 1: Sound

1. Sound is a vibration that travels through a transmission medium such as a gas, liquid, or solid as an acoustic wave.
2. When a sound travels through an elastic material, its speed is defined as the distance it travels per unit of time.
3. The speed of sound in the air is approximately $343m/s$.

Step 2: The major three factors that influence sound speed are:

1. The density of medium: The density of a medium determines the speed of sound; the larger the density of a medium, the slower the speed of sound. Because air is highly compressible, the speed of sound in air is low.
2. The elasticity of the medium: In fluids, the speed of sound is determined by the bulk modulus $\beta$, which is expressed as $v\propto \sqrt{\beta }$. In the solid, the speed of sound depends on Young’s modulus of elasticity $Y$. And the gaseous medium speed of sound depends upon $\gamma$ which is an adiabatic index and its related as $v\propto \sqrt{\gamma }$ .
3. Temperature and pressure of medium: Sound waves travel quicker at higher temperatures because molecular vibrations occur more frequently at higher temperatures. The speed of sound does not depend on the pressure of a medium at a constant temperature.

Hence, the speed of sound in a median depends upon the density of the medium, elasticity of the medium, temperature, and pressure of the medium.