Question

if the pressure of gas at constant temperature is increased four times how the velocity of sound in the gas will be affected​

Answer 1

Answer:

pressure has a direct effect on the velocity of sound in a gas. The velocity of sound is equal to the root of ratio of pressure to the density of the gas. So if the pressure becomes four times, the velocity of sound becomes twice of the initial velocity. It remains constant at constant temperature.

Answer 2

The new velocity of sound will becomes two times of the initial value.

Explanation:

• The velocity of sound in terms of pressure is given by :

$v=\sqrt{\dfrac{\gamma P}{\rho}}$

$\gamma$ is adiabatic constant

P is pressure

$\rho$ is density of medium

It implies,

$v\propto \sqrt{P} \\\\v= k\sqrt{P}$

• If the pressure of gas at constant temperature is increased four time, P' = 4P

• New speed of sound is given by :

$v'= k\sqrt{P'}\\\\v'= k\sqrt{4P}\\\\v'=2k\sqrt{P}\\\\v'=2\times v$

• So, the new velocity of sound will becomes two times of the initial value.

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