JAMB - Physics (2005 - No. 44)
The velocity of sound in air will be doubled if it's absolute temperature is
Quadrupled
Constant
Halved
Doulbed
Explication
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.
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.