Question

Calculate the bulk modulus of air from the following data about a sound wave of wavelength 35 cm 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 simple harmonic motion of amplitude $5.5\times {10}^{-6}m$.

Answer 1

We know that,

Bulk modulus

$B=\frac{\Delta p}{\left(\frac{\Delta v}{v}\right)}=\frac{p_0\lambda }{2\pi S_0}$

where $P_0$ =pressure amplitude,

$P_0=1.0\times {10}^5$

$\Rightarrow$ displacement amplitude

$=S_0=5.5\times {10}^{-6}m$

$\Rightarrow B=\left(\frac{14\times 35\times {10}^{-2}m}{2\pi \left(5.5\right)\times {10}^{-6}m}\right)$

$=1.4\times {10}^{5}N/m^2$