The ratio of densities of oxygen and nitrogen is 16`:`14. At what temperature, the speed of sound in oxygen will be equal to its speed in nitrogen at `14^(@)C`?

Options

A. `35^(@)C`
B. `48^(@)C`
C. `65^(@)C`
D. `14^(@)C`

Answer

D

Explanation

`v=sqrt((gammaP)/(rho))implies(T_(N_(2)))/(T_(O_(2)))=(rho_(N_(2)))/(rho_(O_(2)))implies (T_(N_(2)))/(273+55)=(14)/(16)=(7)/(8)`
`implies T_(N_(2))=287-273=14^(@)C`.