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
Suppose the rate of change of air temperature is $-0.11 \frac{K}{min}$.
Find the rate of change of the speed of sound with respect to time.
Find the rate of change of the speed of sound with respect to temperature.
I found the answer to part one by taking the derivative of the original function:
$ v'= 0.6(T')$
$v'=0.6(-0.11)$
$v'= -0.066 \frac{m/s}{min}$
What I know about part two:
Units are in $\frac{m/K}{min}$
$0.6$ is in units of $\frac{m/s}{K}$
What I have tried:
Since I know the units are in $\frac{m/K}{min}$ , I hypothesized changing the units of $-0.11 \frac{K}{min}$ into $\frac{K}{s}$ in order to cancel out the unit of $s$ to arrive at units in $\frac{m/K}{min}$
$v'=0.6 \frac{m/s}{K}\cdot-0.0011 \frac{K}{s}$
$v' = -0.00066$
This is not the correct answer. Can someone put me on the right track to arrive at $\frac{m/K}{min}$? Is my hypothesis wrong?