Question

The velocity of sound in air increase for every $1^{o}C$ rise in temperature approximately by:

Answer 1

$v\alpha \sqrt{T}$

At NTP,

$\frac{v_t}{v_o}=\sqrt{\frac{273+t}{273+0}}=\sqrt{1+\frac{t}{273}}$

when $t$ is small,

$\frac{v_t}{v_o}\approx 1+\frac{t}{546}$

Putting $v_o=331$m/s

$v_t=(331+0.61t)m/s$

i.e for small temperature variation at $0^{\circ }$, velocity of sound changes by $0.61$ m/s when temperature changes by $1^{\circ }$