Question

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

Correct Answer - D
The speed of sound in gaseous medium is gien by
`v = sqrt((gamma p)/(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)` or `V = (M)/(rho)`
Where `M` is the molecular weight of the gas.
`:.` Eq.(ii) becomes
`(pM)/(rho)` = constant
or `(p)/(rho)` = constant as `M` is a constant
Therefore, from Eq. (i), we have
`v = "constant" xx sqrt(gamma)`
Thus, change inair pressure does not effect the speed of sound. Reason is clear from Eq. (i).