Question

Velocity of sound in a gaseous medium is 330 ms\(^{-1}\). If the pressure is increased by 4 times without change in temperature, the velocity of sound in the gas is

• A. 330 ms\(^{-1}\)
• B. 660 ms\(^{-1}\)
• C. 156 ms\(^{-1}\)
• D. 990 ms\(^{-1}\)

Hint:

For gases, the velocity of sound depends on the temperature and the medium's properties, but in this case, with constant temperature, the velocity remains unchanged even if pressure increases.

Answer 1

The Correct Option is A

The velocity of sound in a gas is given by the equation: \[ v = \sqrt{\frac{\gamma \cdot P}{\rho}} \] where \(v\) is the velocity of sound, \(P\) is the pressure, \(\gamma\) is the adiabatic index, and \(\rho\) is the density of the gas. When the pressure is increased by a factor of 4, without changing the temperature, the density also increases in proportion to the pressure. However, since the temperature does not change, the velocity of sound remains the same. Therefore, the velocity of sound will still be 330 ms\(^{-1}\).