Question

What must be the pressure amplitude in a sound wave in the air (0∘C) if the air molecules undergo a maximum displacement equal to the diameter of an oxygen molecule, about 3.0⋅10−10m?

Answer 1

Answer:

Pressure amplitude, $P=4.42\times 10^{-5}\ Pa$

Explanation:

It is given that,

The maximum displacement equal to the diameter of an oxygen molecule, $d=3\times 10^{-10}\ m$

Speed of sound at 0 degrees is, v = 331.5 m/s

The pressure amplitude for the longitudinal wave is given by :

$P=2\pi f\rho vd$

Where

$\rho$ is the density of air, $\rho=1.2\ kg/m^3$

f is the frequency say 59 Hz

So, pressure amplitude is given by :

$P=2\pi \times 59\times 1.2\times 331.5\times 3\times 10^{-10}$

$P=4.42\times 10^{-5}\ Pa$

So, the pressure amplitude in a sound wave in the air must be $P=4.42\times 10^{-5}\ Pa$. Hence, this is the required solution.