Question

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

• A. $1184\, ^?C$
• B. $1148\, ^?C$
• C. $2184\, ^?C$
• D. $2148\, ^?C$

Answer 1

Answer: (C)

$2184\, ^?C$

Answer 2

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 $t= 2184\,^{\circ}C$