Which one of the following statements is correct?

The speed of sound waves in a medium depends upon the elastic property of the medium but not on inertia property.

The speed of sound waves in a medium depends upon the inertia property of the medium but not on elastic property.

The speed of sound waves in a medium depends neither on its elastic property nor on its inertia property.

The speed of sound waves in a medium depends both on elastic and inertia properties of the medium.

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Answer is Wrong!

This question was previously asked in

UPSC NDA-2 – 2016

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The speed of sound waves in a medium is determined by the medium’s properties related to elasticity and inertia. Sound waves are mechanical waves, meaning they propagate through a medium by causing particles of the medium to oscillate. The elastic property (like Bulk modulus or Young’s modulus) determines how easily the medium restores its shape or volume after being deformed by the wave. The inertia property (density) determines how much resistance the medium offers to changes in motion. The speed of sound increases with increasing elasticity and decreases with increasing density. Therefore, the speed of sound depends on both properties.

Speed of mechanical waves depends on the elastic modulus and density of the medium. Higher elasticity allows faster propagation of disturbances. Higher density provides more inertia, resisting quick motion.

The formula for the speed of sound in a fluid is $v = \sqrt{B/\rho}$, where B is the Bulk modulus and $\rho$ is the density. For a solid rod, $v = \sqrt{Y/\rho}$, where Y is Young’s modulus. These formulas explicitly show dependence on both an elastic property and density.

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