The speed of sound in air at temperature T an | vedclass

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(C) The speed of sound in an ideal gas is given by the formula $v = \sqrt{\frac{\gamma R T}{M}}$.From this relation, it is clear that the speed of sou

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$\sqrt{2} v$

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(C) The speed of sound in an ideal gas is given by the formula $v = \sqrt{\frac{\gamma R T}{M}}$.From this relation, it is clear that the speed of sound $v$ is independent of pressure $p$ and is directly proportional to the square root of the absolute temperature $T$, i.e.,$v \propto \sqrt{T}$.Given initial conditions: $T_1 = T$ and $v_1 = v$.Given final conditions: $T_2 = 2 T$ and $p_2 = \frac{p}{2}$.Since $v$ is independent of pressure, the change in pressure does not affect the speed.Using the proportionality $v \propto \sqrt{T}$, we have:$\frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}}$$\frac{v_2}{v} = \sqrt{\frac{2 T}{T}} = \sqrt{2}$Therefore, $v_2 = \sqrt{2} v$.

The speed of sound in air at temperature $T$ and pressure $p$ is $v$. When the temperature is increased to $2 T$ and the pressure is reduced to $\frac{p}{2}$, then the speed is changed to

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