Effect of temperature on speed of sound

Question

Formula for calculating speed of sound in dry air is

$$V(t)=V(0)+0.61t$$

The temperature here is always taken in Celsius .Why don't we use kelvin?

Answer 1

The speed of sound in an ideal gas is given by:

$$ v = \sqrt{\gamma RT} $$

Suppose we want to calculate the speed near some reference temperature $T_0$, i.e. the temperature is $T = T_0 + \delta T$ where $\delta T$ is small. We rewrite the equation for the velocity as:

$$ v = \sqrt{\gamma R(T_0 + \delta T} $$

and then rearrange this to:

$$ v = \sqrt{\gamma R T_0} \left(1 + \frac{\delta T}{T_0}\right)^{1/2}$$

Then because $\delta T \ll T_0$ we can expand the square root using a binomial expansion to get:

$$ v \approx \sqrt{\gamma R T_0} \left(1 + \frac{1}{2}\frac{\delta T}{T_0}\right) $$

But the term $\sqrt{\gamma R T_0}$ is just the velocity at the temperature $T_0$ so our equation becomes:

$$ v \approx v(T_0) + \frac{1}{2}\sqrt{\frac{\gamma R}{T_0}}\delta T $$

and that's how we get the approximate equation you cite. The particular case when $T$ is given in Celcius just comes from taking $T_0 = 273.15$K so there is nothing special about it - it's just a convenient choice of $T_0$.