Question

Assertion: Variation in air pressure do not affect the speed of sound when temperature remains constant
Reason : Speed of sound is directly proportional to square root of pressure

• A. If both assertion and reason are true and reason is the correct explanation of assertion.
• B. If both assertion and reason are true but reason is not the correct explanation of assertion.
• C. If assertion is true but reason is false
• D. If both assertion and reason are false

Answer 1

Answer: (B)

Speed of sound, $v=\sqrt{\frac{\gamma P}{\rho}}$.
For a given gas, if $\rho$ remains same, the velocity would increase with increase in pressure. But at constant temperature, change in pressure is accompanied by change in volume. So, $\frac{P}{\rho}$ remains constant
The correct reason is that P and $\rho$ vary in the same manner and the velocity of sound depends upon the ratio $\frac{P}{\rho}$