Question

The speed of sound in air at 00c is 332 m/s. if it increases at the rate of 0.6 m/s per degree, what will be the temperature when the velocity has increased to 344 m/s?

Answer 1

sound waves v = sqrt (P/rho) P is the pressure and rho is the density.Write this as v1 = root(p1/rho) v2= root (p2/rho) square both sides v1^2 = p1 /rho v2^2 = p2/rho Take the ration v1^2/v2^2 = p1/p2 Put the values v1=1 and v2 = 2 YOu get 1/4 = p1/p2 p1 = n kb T1 and p2= n kb T2. Here n is the number density. kb Boltzmann constant and T1 and T2 are temperatures. If you use it in the above equation you get T2= 4 T1 T1 is 27 degrees= 273 + 27 = 300 T2= 1200 degrees = 1200-273 = 927 degrees