The speed of sound v in air is a function of the temperature

The speed of sound, v, in air is a function of the temperature, T, of the air: v = 331.4 + 0.6(T 273) with v in meters per second and T in kelvins (WebAssign abbreviation K). Suppose the rate of change of air temperature is -0.11 K/min. 1. Find the rate of change of the speed of sound with respect to time. 2. Find the rate of change of the speed of sound with respect to temperature.

Solution

A.

v = 331.4 + 0.6*(T - 273)

dv/dT = 0 + 0.6 m/sec.K

Given

dT/dt = -0.11 K/min = -0.11/60 K/sec

dT/dt = -0.001833 K/sec

Using both bold equations:

dv/dt = - 0.6*0.001833 m/sec^2

dv/dt = -0.0010998 m/sec^2

B.

dv/dT = 0.6 m/sec.K