Question

Show that for every 10 C rise in temperature, the velocity of sound in air increases by 0.61 ms–1.

Answer 1

velocity of sound is given as $v=\sqrt{\frac{\gamma RT}{M}}$

here it is clear that, velocity of sound is directly proportional to square root of temperature.

so, v ∝ √T

⇒v ∝ √(t + 273°C)

⇒v1/v2 = √{(t + 273)/273}

⇒v1/v2 = {1 + t/273}½

when t is very small, 1 >> t/273

so, v1/v2 = [1 + t/546]

we know, velocity of sound at NTP is 332m/s so, v2 = 332

so, v1 = 332[1 + t/546]

= 332 + 332t/546

= 332 + 0.61t

for increasing temperature by 1°C, velocity increases by 0.61 m/s .

here it clearly shown that, for every 1° C rise in temperature, the velocity of sound in air increases by 0.61 m/s.