Prove that speed of sound in air increases by `0.61 ms^(-1)` per degree celsius rise in temperature.

Explanation

Since `v prop sqrt(T)`
the speed of sound changes directly to the square root of temperature in kelvin.
Let `v_(0)` be the speed of sound at temperature at `0^(@)C ` or `273 K`. Let v the speed of sound at any arbitrary temperature T (in kelvin,) then
`(v)/(v_(0))= sqrt((T)/(273))= sqrt((273+t)/(273))`
`v=v_(0) sqrt(1+(t)/(273))=v_(0)(1+(t)/(546))`
(Using binomial expansion)
Since `v_(0)=331 ms^(-1)` at `0^(@)C`, v at a particular temperature in `t^(@)C` is
`v=(331+0.60t) ms^(-1)`
Thus the speed of sound in air increases by `0.61 ms^(-1)` per degree celsius in temperature.