The velocity of sound in air at $15^{0} C$ is $v_{1}$ . If the temperature (on the absolute scale) is doubled and the pressure halved, the velocity is $v_{2}$ . Then $v_{1} : v_{2}$ is:

1 : 1

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1 : 2

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1 : \sqrt{2}

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\sqrt{2} : 1

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Solution

The correct option is D $1 : \sqrt{2}$
Velocity of sound in air is given by $v = \sqrt{\frac{γ R T}{M}}$
$⟹$ $v = \sqrt{T}$ $(∵ γ, R, M$ are $c o n s t a n t s)$
Given : $T_{1} = T$ and $T_{2} = 2 T$
$∴$ $v_{1} : v_{2} = \sqrt{T_{1}} : \sqrt{T_{2}} = \sqrt{T} : \sqrt{2 T}$
Or $v_{1} : v_{2} = 1 : \sqrt{2}$

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