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 $(1.0\times {10}^{5}and14)$ Pa and the particles of the air vibrate in simple harmonic motion of amplitude $5.5\times {10}^{-6}$ m.

• A. $3.2\times {10}^2\frac{N}{m^2}$
• B. $5.5\times {10}^6\frac{N}{m^2}$
• C. $1.4\times {10}^5\frac{N}{m^2}$
• D. None of these

Answer 1

The correct option is C

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

Given

Wavelength $\lambda =35$cm

=$35\times {10}^{-2}$m

$\Delta P=(1.0\times {10}^5-14)Pa$

so$P_0=14Pa$

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

To find Bulk modulus

Relation between pressure and displacement amplitude

$P_0=BK{S}_{0}K=\frac{2\pi }{\lambda }$

$14=B\frac{2\pi }{35\times {10}^{-2}}\times 5.5\times {10}^{-6}$

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