Question

Assertion :The decrease in speed of sound at high altitudes is due of fall in pressure at this altitude. Reason: The speed of sound is the same at all pressures and varies with temperature only.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is incorrect but Reason is correct
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is C Assertion is incorrect but Reason is correct

The speed of sound in a gas is given by,

$v=\sqrt{\gamma P/d}$,.................................eq1

where $\gamma =$ ratio of specific heats of gas at constant pressure and constant volume

$P=$ pressure of the gas,

$d=$ density of the gas,

now by a gas equation,

$PV=RT$$, (for 1 mole of gas),

where $V=$ volume of the gas,

$V=M/d$$, (M=molecular mass of the gas),

hence $P/d=RT/M$

therefore $v=\sqrt{\gamma RT/M}$,...................................eq2

by eq1 we can think that speed depends upon pressure $P$ but actually it

doesn't happen because at a constant temperature,

$P/d=RT/M=$ constant,

therefore speed doesn't decrease with pressure decrease i.e. assertion is incorrect . But eq2 shows that speed varies with temperature i.e. reason is correct.