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Q.
At what temperature will the speed of sound in air be $3$ times its value at $0\,{}^°C$?
Waves
Solution:
Speed of sound in air is
$v = \sqrt{\frac{\gamma RT}{M}}$
where $T$ is the absolute temperature.
Since $\gamma$ and $M$ are constants
$\therefore v \propto \sqrt{T}$
$\Rightarrow \frac{v_{t}}{v_{0}} = \sqrt{\frac{273 + t}{273}}$
$\Rightarrow \frac{3v_{0}}{v_{0}} = \sqrt{\frac{273 + t}{273}}$
Squaring both sides, we get
$9 = \frac{273 + t}{273}$ or
$2457 = 273 + t$ or $t= 2184\,{}^{\circ}C$