Question

Calculate the bulk modulus of air from the following data for a sound wave of wavelength $35cm$ travelling in air. The pressure at a point varies between $(1.0\times {10}^5\pm 14)$ Pa and the particles of the air vibrate in $SHM$ of amplitude $5.5\times {10}^{-6}m$.

Answer 1

We know that,
Bulk modulus $B=\frac{\Delta p}{\left(\Delta V/V\right)}=\frac{P_0\lambda }{2\pi S_0}$
Where $P_0$= pressure amplitude $\Rightarrow P_0=1.0\times {10}^5$
$S_0$= displacement amplitudes $\Rightarrow S_0=5.5\times {10}^{-6}m$
$\Rightarrow B=\frac{14\times 35\times {10}^{-2}m}{2\pi \left(5.5\right)\times {10}^{-6}m}=1.4\times {10}^{5}N/m^2$.