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

$v = \sqrt{\frac{\lambda RT}{M}}$

Where T is the absolute temperature.

Since $\gamma$and $M$are constant.

$\therefore v \propto \sqrt{T}$

$\Rightarrow \frac{v_{t}}{v_{0}} = \sqrt{\frac{273 + t}{273}}$

$\frac{3v_{0}}{v_{0}} = \sqrt{\frac{273 + t}{273}}$

Squaring both sides, we get

$9 = \frac{273 + t}{273}or2457 = 273 + tort = 2184{^\circ}C$