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)

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