Question

Speed of sound does not depend upon:
(A) Pressure
(B) Temperature
(C) Medium
(D) Humidity

Answer 1

Hint: Sound is a mechanical wave that propagates through a medium, it is transmitted via the individual molecules present in a medium, so the properties of the molecules present in the medium define how well the sound can travel in it.

Complete step by step solution:
A sound wave travels when the molecules of a medium vibrate, the inertia and the elasticity of the medium plays a significant role to determine the speed of sound. The speed of sound in a gaseous medium (air) is given by-
$v = \sqrt {\dfrac{{\gamma RT}}{\mu }} $
Where v is the velocity of the sound wave,
$\gamma $is the adiabatic index of the medium,
R is the gas constant
$\mu $is the molar mass of the medium
And T is the temperature
Now on studying the options one by one we have-
Pressure- At a constant temperature, the speed of sound does not depend on the pressure.
Temperature- From the formula it is evident that the speed of sound is directly proportional to the root of temperature of the medium, it varies as-
$v \propto \sqrt T $
Thus an increase in the temperature of the medium increases the speed of the sound.
Medium- The speed of sound is different in different mediums- the speed is maximum in solids and the minimum in the liquids. For solids the speed depends on the young’s modulus of the material, for liquids it is the bulk modulus of the material and for gases it is the adiabatic index, gas constant and temperature.
Humidity- If the amount of water is increased in the air, the density of air decreases. Here, It is assumed that the air molecules are the medium through which sound travels and if humidity is introduced in a medium, for a constant temperature and pressure the number of air molecules would be less per unit area, thus a decrease in the density of air. Since the speed of sound depends on the density of the material as-
$v \propto \dfrac{1}{{\sqrt \rho }}$, thus the velocity would increase here. Hence, speed of sound depends on the humidity, although the change produced is very less.

It is clear that the speed of sound does not depend on the pressure of the medium thus option (A) is correct.


Note: In the formula for the velocity, the value of $RT$can be replaced by $PV$and the numerator and the denominator are divided by V, it becomes-
$v = \sqrt {\dfrac{{\gamma P}}{\rho }} $ but it is not possible to change the pressure of the medium without changing its temperature. So the pressure does not affect the speed of sound.