Question

The pressure at a point varies from `99980 Pa` to `100020 Pa` due to simple harmonic sound wave. The amplitude and wavelength of the wave are `5 xx 10^(-6) m` and `40 cm` respectively. Find the bulk modulus of air

Answer 1

Given 

P₁ = 99980 Pa

P₂ = 100020 Pa

Then

\(\Delta\)P = 100020 - 99980

\(\Delta\)P = 40

Then 

Bulk molecule,

\(\beta = \frac{\Delta P\lambda}{2\pi S_0}\)

\(\beta = \frac{20 \times 40\times 10^{-2}}{2 \times 3.14 \times 5 \times 10^{-6}}\)

\(\beta = \frac{800\times 10^{-2}}{31.4 \times 10^{-6}}\)

\(\beta = 25.47 \times 10^4 N/m^2\)