Question

Assertion: The speed of sound in solids is maximum though density is large.
Reason: The coefficient of elasticity of solids is large.
(A) Both assertion and reason are true and reason is the correct explanation of assertion.
(B) Both assertion and reason are true but reason is not the correct explanation of assertion.
(C) Assertion is correct but reason is incorrect.
(D) Assertion and reason both are incorrect.

Answer 1

Hint : Sound waves travel through a medium by alternately contracting and expanding the parts of the medium in which it travels. This depends on the characteristics of the medium through which the propagation takes place.

Formula used: The following formulas are used to solve this question.
$v = \sqrt {\dfrac{\gamma }{\rho }}$ where $v$ is the velocity of sound in solids, $\rho$ is the density of solids and $\gamma$ is the Young’s modulus.

Complete step by step answer:
The speed of sound is the distance travelled per unit time by any sound.
The speed of sound is defined as the dynamic propagation of sound waves. The speed of sound in solids is given by,
$v = \sqrt {\dfrac{\gamma }{\rho }}$ where $v$ is the velocity of sound in solids, $\rho$ is the density of solids and $\gamma$ is the Young’s modulus.
As evident from the formula, ${v^2}\alpha \dfrac{1}{\rho }$ , i.e. the density of solid is inversely proportional to the square of the velocity of sound through it.
We know that, ${\rho _{solid}} > {\rho _{liquid}} > {\rho _{gas}}$ . Thus the density of solid is maximum.
$\therefore$ The velocity of sound through solid should be least.
But, here comes in the value of $\gamma$ , the Young’s modulus.
Elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate loads are applied to them; if the material is elastic, the object will return to its initial shape and size after removal.
The Young’s modulus or the modulus of elasticity in tension is a mechanical property that measures the tensile stiffness of a solid material. It quantifies the relationship between tensile stress $\sigma$ (force per unit area) and axial strain $e$ (proportional deformation) in the linear elastic region of a material and is determined using the formula-
$\gamma = e\sigma$ .
The value of Young’s modulus is so large that they are measured in Giga-pascals, implying that, velocity of sound $v$ is maximum in case of solids.
$\therefore$ Both assertion and reason are true and reason is the correct explanation of assertion.
The correct answer is Option A.

Note:
Sound is nothing more than a disturbance which is propagated by the collisions between the particles; one molecule hitting the next and so forth. Solids are significantly denser than liquids or gases. This means that the molecules are closer to each other in solids than in liquids and in liquids than in gases. This closeness due to density means that they can collide very quickly. Effectively it takes less time for a molecule of a solid to bump into its neighbouring molecule. Due to this advantage, the speed of sound in a solid is larger than in a gas.
Speed of sound in solid is 6000 metres per second while the speed of sound in steel is equal to 5100 metres per second. Another interesting fact about the speed of the sound is that sound travels 35 times faster in diamonds than in the air.