The velocity of sound in air at 20^{circ} C a | vedclass

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(B) The velocity of sound in an ideal gas is given by the formula $v = \sqrt{\frac{\gamma RT}{M}}$, where $\gamma$ is the adiabatic index, $R$ is the

Vedclass · Accepted Answer

$356$

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(B) The velocity of sound in an ideal gas is given by the formula $v = \sqrt{\frac{\gamma RT}{M}}$, where $\gamma$ is the adiabatic index, $R$ is the universal gas constant, $T$ is the absolute temperature in Kelvin, and $M$ is the molar mass of the gas. Note that the velocity of sound is independent of pressure for an ideal gas. Given: $T_1 = 273 + 20 = 293 	ext{ K}$ $T_2 = 273 + 40 = 313 	ext{ K}$ $v_1 = 344.2 	ext{ m/s}$ Using the ratio: $\frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}}$ $v_2 = v_1 \sqrt{\frac{313}{293}}$ $v_2 = 344.2 	imes \sqrt{1.06826}$ $v_2 \approx 344.2 	imes 1.03356$ $v_2 \approx 355.75 	ext{ m/s} \approx 356 	ext{ m/s}$.

The velocity of sound in air at $20^{\circ} C$ and $1 \text{ atm}$ pressure is $344.2 \text{ m/s}$. At $40^{\circ} C$ and $2 \text{ atm}$ pressure, the velocity of sound in air is approximately: (in $\text{ m/s}$)

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