Question

the velocity of sound in air at 14 degree centigrade is 340m/s. what will it be when the pressure of the gas is double and its temperature is raised to 150 7.5 degree centigrade?

Answer 1

this is just a example
What is the temperature at which the velocity of sound in air is twice its velocity at 10C?


answer

The speed of sound Cs depends on pressure (P) and density (ρ) as follows:

Cs =√(γP/ρ)

Where γ is the adiabatic constant ( the ratio between heat capacities at constant pressure and at constant volume =1.4 for air).

Assuming the air is an ideal gas, its density is inversely proportional to the absolute temperature (T in Kelvin), for constant pressure.

For T1 = 10◦C = 10 +273=283K, Cs = Cs1

Now if we increase the absolute temperature 4 fold to T2 = 4T1 =4*283K = 1132K

Then ρ will decrease 4 fold and hence Cs will double.

Cs2 = 2Cs

Now to get back to Celsius degrees: 1132 -273 = 859◦C

So, the answer is that at T = 859◦C the speed of sound will be double that at 10◦C

I hope this will help you