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Q.

The speed of sound in air at temperature T and pressure P is V. When the temperature is increased to 2T and the pressure is reduced to $\frac{P}{2}$ , then the speed is changed to

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a

$\frac{V}{\sqrt{2}}$

b

$\sqrt{2} V$

c

2V

d

V

answer is C.

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Detailed Solution

We know

$V \propto \sqrt{T} \Rightarrow \frac{V_{2}}{V_{1}} = \sqrt{\frac{T_{2}}{T_{1}}}$

$\frac{V_{2}}{V} = \sqrt{\frac{2 T}{T}} \Rightarrow V_{2} = \sqrt{2} V$

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