At what temperature will the speed of sound be nearly 1.5 times its value at N.T.P.?

Question

Aicharya · Accepted Answer

Speed of sound depends on $T$ temperature, $M$ molar mass and $\gamma$ gas exponent: $\begin{aligned} & v=\sqrt{\frac{\gamma R T}{M}} \ & \Rightarrow \frac{v^{\prime}}{v}=\sqrt{\frac{T^{\prime}}{T}}=1.5 \ & \Rightarrow \sqrt{T^{\prime}}=1.5 \sqrt{(273)} \ & T^{\prime}=2.25 	imes 273 \mathrm{~K}=614 \mathrm{~K} \end{aligned}$ On writing in degree Celsius: $T^{\prime}=341^{\circ} \mathrm{C}$

At what temperature will the speed of sound be nearly 1.5 times its value at N.T.P.?

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