What is the effect of temperature on the velocity of sound?Derive the relation.

Explanation

We know that resistance of a wire increases with rise in temperature. At temperature .T., resistance of the metal wire `(R_(T))` is given as
`R_(T) = R_(0) (1+ alpha T)`
`rArr R_(T)- R_(0) = R_(0) alpha T` ..(1)
where `R_(0)`= Resistance of metal wire at `0^(@)C`.
If `R_(100)`= Resistance of the same metal wire at `100^(@)C` then `R_(100)- R_(0)= R_(0) alpha (100)` ...(2)
Divide eqn (1) by (2)
`(R_(T)-R_(0))/(R_(100)-R_(0))= (R_(0)alpha T)/(R_(0) alpha (100))`
`rArr T= ((R_(T) - R_(0))/(R_(100)- R_(0))) xx 100`
In a metre bridge, in place resistance S by setting the given metal wire, we can find its resistance first keeping the temperature at `0^(@)C` and then at `100^(@)C`. So `R_(0) and R_(100)` can be found out with the help of metre bridge. Now by keeping the given metal wire at unknown temperature in place of S in metre bridge, we can find `R_(T)` and so by knowing the values of `R_(0), R_(100) and R_(T)` we can find the unknown temperature T.