Question

At what temperature velocity of sound in air will be four times the velocity of ------------------- in air at N.T.P? [note: at N.T.P , temperature = 0 degrees Celsius.

Answer 1

Velocity of sound at temperature T°C is given by

$V=20.05 \sqrt{273.15+T }$

temperature at NTP = 0°C
$V_0=20.05 \sqrt{273.15+0}=331.3\ m/s$

Let at temperature T°C, the velocity become 4 times
V = 331.3*4 = 1325.2 m/s

$1325.2 = 20.05 \sqrt{273.15+T}\\ \\ \frac{1325.2}{20.05}= \sqrt{273.15+T}\\ \\66.1=\sqrt{273.15+T}\\ \\ 273.15+T=66.1^2=4369.21\\ \\T = 4369.21-273.15=4096.06\ ^0C$

So at 4096.06°C, velocity of sound will be 4 times that of velocity of air at NTP.