Which of the following represent the correct variation of speed . . .

Question : Which of the following represent the correct variation of speed (v) of sound with the pressure (P) in a gas at a constant temperature?

Doubt by Yathartha & Zoha

DAV 2023

Solution : 

According to Laplace formula for speed of sound in air is given by 
v = √(γP/ρ)
At constant temperature
PV = constant
P(m/ρ) = constant [∵Volume = mass/density]
i.e. P/ρ = constant [∵ mass (m) is constant

When Pressure changes then density also changes by the same ratio. Hence the factor P/⍴ remains constant. Therefore, pressure has no effect on the speed of sound in a gas.

We can say that speed of sound in air is independent of pressure of gas at constant temperature. 

Hence, d) would be the correct option.