The velocity of sound in air will be doubled if it's absolute temperature is
A
Quadrupled
B
Constant
C
Halved
D
Doulbed
Verified Correct Answer: A.
Physical Principles & Numerical Solution
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, its absolute temperature will be quadrupled.
Source: Myschool Past Questions Archive (Record #41430)