The temperature at which the speed of sound in air becomes double of its value at $27^{\circ}$ C is

54^oC

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327^oC

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927^oC

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-123^oC

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Solution

The correct option is C $927^{0} C$
Let v be the speed of sound and T represent temperature.
We know that speed of sound is directly proportional to square root of temperature.
$v = \sqrt{\frac{γ R T}{M}} \Rightarrow v \propto \sqrt{T}$
i.e. if v is doubled then T becomes four times,
$T_{1} = 27 + 273 = 300 K, T_{2} = ?$
At $T_{2}, v b e c o m e s 2 v$
$\frac{v}{2 v} = \frac{\sqrt{T_{1}}}{\sqrt{T_{2}}}$
$∴ \frac{1}{4} = \frac{T_{1}}{T_{2}}$
$∴ T_{2} = 4 T_{1}$
$∴ T_{2} = 4 (300 K) = 1200 K$

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