Question

At what temperature will the velocity of sound in air be doubled than Velocity in air at 0°C.

PLEASE EXPLAIN WITH FULL STEPS...

Answer 1

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