Question

Calculate the bulk modulus of air from the following data about a sound wave of wavelength $35cm$ travelling in air. The pressure at a point varies between $\left(1.0\times {\left(10\right)}^5\pm 20\right)Pa$ and the particle of the air vibrate in simple harmonic motion of amplitude $5.6\times 10^{-6}m.$

• A. $4\times 10^6$
• B. $4\times 10^4$
• C. $4\times 10^8$
• D. $4\times 10^2$

Answer 1

Answer: (B)

$\Delta P_0=20Pa$
${\delta }_0=5.6\times 10^{-6}m$
$\lambda =35cm\Rightarrow 35/100m$
$k=\frac{2\pi }{\lambda }\Rightarrow \frac{2\pi }{35}\times 100$
$k=\frac{40\pi }{7}$
$\Delta P_0=Bk{\delta }_0$
$B=\frac{\Delta P_0}{k{\delta }_0}$
$=\frac{7\times 20}{40\pi \times 5.6\times 10^{-6}}=\frac{1}{25}\times 10^{6}N/m^2$
$B=4\times 10^{4}N/m^2$