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

Prove that speed of sound in air increases by 0.61 ms^(-1) per degree

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