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)

$\Delta P_{0}=20Pa$
$\delta_{0}=5.6\times 10^{- 6}m$
$\lambda =35cm\Rightarrow 35/100m$
$k=\frac{2 \pi }{\lambda }\Rightarrow \frac{2 \pi }{35}\times 100$
$k=\frac{40 \pi }{7}$
$\Delta P_{0}=Bk\delta_{0}$
$B=\frac{\Delta P_{0}}{k \delta_{0}}$
$=\frac{7 \times 20}{40 \pi \times 5 . 6 \times 10^{- 6}}=\frac{1}{25}\times 10^{6}N/m^{2}$
$B=4\times 10^{4}N/m^{2}$