At what temperature (in ^circ C) will the spe | vedclass

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(A) The speed of sound in a gas is given by $v = \sqrt{\frac{\gamma RT}{M}}$, which implies $v \propto \sqrt{T}$, where $T$ is the absolute temperatur

Vedclass · Accepted Answer

$2184$

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(A) The speed of sound in a gas is given by $v = \sqrt{\frac{\gamma RT}{M}}$, which implies $v \propto \sqrt{T}$, where $T$ is the absolute temperature in Kelvin.Let $v_1$ be the speed of sound at $T_1 = 0^\circ C = 273 \ K$.Let $v_2$ be the speed of sound at temperature $T_2$ such that $v_2 = 3v_1$.Using the relation $\frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}}$, we get:$\frac{3v_1}{v_1} = \sqrt{\frac{T_2}{273}}$$3 = \sqrt{\frac{T_2}{273}}$Squaring both sides:$9 = \frac{T_2}{273}$$T_2 = 9 	imes 273 = 2457 \ K$.To convert this to Celsius: $T(^\circ C) = T(K) - 273 = 2457 - 273 = 2184^\circ C$.

At what temperature (in $^\circ C$) will the speed of sound in air be $3$ times its value at $0^\circ C$ (in $^\circ C$)?

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