Question

Show that when temperature of air increases by 1 degree C then speed of sound changes by 0.61m/s

Answer 1

Answer:

Speed of Sound

Explanation:

For a 1 degree rise in temperature, the multiplier is obviously sqrt[(T + 1)/T] = (1+1/T)^1/2

Where T Kelvin is the starting Absolute Temperature(Celcius + 273).

By the Binomial Theorem, this expands to:

1 + 1/(2T) + much smaller terms in higher powers of 1/T. These latter terms are negligible for our purposes since for typical room temperature, T = about 290K, and the significant term is only about 1/580 or 0.0017

The increase is approx V/(2T), where V is the speed of sound at the starting temp.

The speed of sound is about 340 in your living room, and the increase is only about 340/580 = 0.59 meters per second approx, for a 1-degree rise in temperature.