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 × 10⁵ ± 14) Pa and the particles of the air vibrate in simple harmonic motion of amplitude 5.5 × 10⁻⁶ m.

Answer 1

Given:
Wavelength of sound wave $\lambda$ = 35 cm = $35\times {10}^{-2}\mathrm{m}$
Pressure amplitude P₀ = $1.0\times {10}^5\pm 14\mathrm{Pa}$
Displacement amplitude of the air particles S₀ = 5.5 × 10⁻⁶ m
Bulk modulus is given by:
$B=\frac{P_0\lambda }{2\pi S_0}=\frac{∆p}{\left(∆V/V\right)}$
On substituting the respective values in the above equation, we get:
$$\begin{gathered} B=\left(\frac{14\times 35\times {10}^{-2}\mathrm{m}}{2\mathrm{\pi }\left(5.5\right)\times {10}^{-6}\mathrm{m}}\right) \\ \Rightarrow B=1.4\times {10}^5\mathrm{N}/{\mathrm{m}}^2 \end{gathered}$$

Hence, the bulk modulus of air is 1.4$\times$10⁵ N/m².