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(B) The speed of sound in a gas is given by the formula $v = \sqrt{\frac{\gamma P}{\rho}}$, where $\gamma$ is the adiabatic index, $P$ is the pressure

Vedclass · Accepted Answer

$1.96$

Vedclass · Answer

(B) The speed of sound in a gas is given by the formula $v = \sqrt{\frac{\gamma P}{\rho}}$, where $\gamma$ is the adiabatic index, $P$ is the pressure, and $\rho$ is the density of the gas.Given that the density $\rho$ remains constant, the speed of sound $v$ is directly proportional to the square root of pressure, i.e.,$v \propto \sqrt{P}$.Let $v_1$ be the speed of sound at pressure $P_1$ and $v_2$ be the speed of sound at pressure $P_2$.Then, $\frac{v_2}{v_1} = \sqrt{\frac{P_2}{P_1}}$.According to the problem, $v_2 = 1.4 v_1$, so $\frac{v_2}{v_1} = 1.4$.Substituting this into the equation: $1.4 = \sqrt{\frac{P_2}{P_1}}$.Squaring both sides, we get: $(1.4)^2 = \frac{P_2}{P_1}$.Therefore, $\frac{P_2}{P_1} = 1.96$.

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