The velocity of sound in air will be doubled if it's ...
The velocity of sound in air will be doubled if it's absolute temperature is
Quadrupled
Constant
Halved
Doubled
Correct answer is A
In general, the velocity of sound in air varies directly as the square root of temperature measured in kelvin.
That V \( \propto \sqrt{T} \implies V^2 \propto T. \\
\text{Therefore} \frac{V^2_1}{T_1} = \frac{V^2_2}{T_2} \\
\text{Thus Let } V_1 = 4m/s \\
T_1 = 10K \\
\text{Therefore } V_2 = 2V_1 = 8m/s \\
\implies \frac{4^2}{10} = \frac{8^2}{T_2} \\
T_2 = \frac{64 \times 10}{16} = 40K\\
T_2 = 4T_1 \)
Thus when the velocity of sound in air is doubled, it's absolute temperature will be quadrupled.