Question

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

• A. ${1184}^{o}C$
• B. ${1148}^{o}C$
• C. ${2184}^{o}C$
• D. ${2148}^{o}C$

Answer 1

Answer: (C)

${2184}^{o}C$

Speed of sound in air is
$V=\sqrt{\frac{\gamma RT}{M}}$
where $T$ is the absolate temperature.
since $\gamma$ and $M$ are constant
$\therefore V\alpha \sqrt{T}$
$⟹\frac{V_t}{V_0}=\sqrt{\frac{273+t}{273}}⟹\frac{3V_0}{V_0}=\sqrt{\frac{273+t}{273}}$
Squaring both sides, we get
$9=\frac{273+t}{273}$ or $2457=273+t={2184}^{o}C$