Question

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.

• 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 the Reason is not the correct explanation of the Assertion.
• C. If Assertion is true but Reason is false.
• D. If both Assertion and Reason are false.

Answer 1

Answer: (D)

The speed of sound in gaseous medium is given by
$v=\sqrt{\frac{\gamma p}{\rho }}$ ... (i)
At constant temperature
$pV=$ constant ... (ii)
If $V$ is the volume of one mole of a gas,
then density of gas $\rho =\frac{M}{V}$ or $V=\frac{M}{\rho }$
where $M$ is the molecular weight of the gas.
$\therefore$ Eq. (ii) becomes
$\frac{pM}{\rho }=$ constant
or $\underline{p}=$ constant as $M$ is a constant
Therefore, from Eq. (i), we have
$v=\text{ constant }\times \sqrt{\gamma }$
Thus, change in air pressure does not affect the speed of sound.
Reason is clear from Eq. (i)