A sound wave passing through an ideal gas at NTP produces a pressure change of 0.001 dyne $/ \mathrm{cm}^2$ during adiabatic compression. The corresponding change in temperature $(\gamma=1.5$ for the gas and atmospheric pressure is $1.013 imes 10^6$ dyne $/ \mathrm{cm}^2$ ) is

Question

A sound wave passing through an ideal gas at NTP produces a pressure change of 0.001 dyne $/ \mathrm{cm}^2$ during adiabatic compression. The corresponding change in temperature $(\gamma=1.5$ for the gas and atmospheric pressure is $1.013 	imes 10^6$ dyne $/ \mathrm{cm}^2$ ) is

Aicharya · Accepted Answer

$T^\gamma p^{1-\gamma}=$ constant or $T^\gamma=p^{\gamma-1}$ $\begin{aligned} T & =p\left(\frac{\gamma-1}{\gamma}ight) \ 	herefore \quad \frac{\Delta T}{T} & =\frac{\gamma-1}{\gamma} 	imes \frac{\Delta p}{p} \ \frac{\Delta T}{T} & =\left(\frac{1.5-1}{1.5}ight) 	imes \frac{0.001}{1.013 	imes 10^6} \ \Delta T & =8.98 	imes 10^{-8} \mathrm{~K}\end{aligned}$

A sound wave passing through an ideal gas at NTP produces a pressure change of 0.001 dyne $/ \mathrm{cm}^2$…

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