Question

Ex.27. If the velocity of sound at room temperature is
340 m/s the density of air is 1.2 kg/m3, then
calculate atmospheric pressure
y = 1.4​

Answer 1

The atmospheric pressure, $P=99085.7Nm^{-2}$

Explanation:

Given,

The velocity of sound at room temperature, $V_{s} =340\dfrac{m}{s}$,

the density of air, $\rho= 1.2\dfrac{kg}{m^3}$ and  

$\gamma=1.4$

To calculate, atmospheric pressure, P = ?

We know that,

$V_{s}=\sqrt{\dfrac{\gamma P}{\rho} }$

⇒ $340=\sqrt{\dfrac{1.4\times P}{1.2}}$

Squaring both sides, we get

$340^2=\dfrac{1.4\times P}{1.2}$

⇒ $340^2=\dfrac{7\times P}{6}$

⇒ $P=\dfrac{115600\times 6}{7}$

∴ $P=99085.7Nm^{-2}$

Hence, the atmospheric pressure, $P=99085.7Nm^{-2}$