Assertion: The change in air pressure effects the speed of sound.
Reason: The speed of sound in gases is proportional to the square of pressure.

Options

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

Answer

D

Explanation

The speed of sound in gaseous medium is given by
`v=sqrt((gammaP)/(rho))...(i)`
At constant temperature
PV = constant ...(ii)
If V is the volume of one mole of a gas, then density of gas `rho=(M)/(V)orV=(M)/(rho)`
where M is the molecular weight of the gas.
`therefore` Eq. (ii) becomes
`(PM)/(rho)` = constant
or `(P)/(rho)` = constant as M is a constant
Therefore, from Eq. (i), we have
v = constant `xxsqrt(gamma)`
Thus, change in air pressure does not effect the speed of sound.
Reason is clear from Eq. (i).