Question

Calculate the bulk modulus of air from the following data about a sound wave of wavelength 35 cm traveling in air. The pressure at a point varies between (1 x 10⁵ 土 14) Pa and the particles of the air vibrate in a simple harmonic motion of amplitude 5.5 x 10⁻⁶ m.

Answer 1

Answer ⇒ B = 1.4 × 10⁵ N/m².

Explanation ⇒ We know that,

p₀ = Bks₀,

where B is the bulk modulus ,

p₀ is the pressure amplitude = 14 Pa,

s₀ is the displacement amplitude = 5.5 × 10⁻⁶ ,

and k = 2π/λ

∴ B = p₀/ks₀

∴ B = 14 × 0.35/(2π × 5.5 × 10⁻⁶)

∴ B = 1.4 × 10⁵ N/m².

Hence, the bulk modulus of the air is  1.4 × 10⁵ N/m².

Hope it helps.

Answer 2

Answer : 1.4 × 10⁵ N/m².

Explanation : as we know that,

p₀ = Bks₀,

( B : bulk modulus)

p₀, pressure amplitude = 14 Pa,

s₀, displacement amplitude = 5.5 × 10⁻⁶ ,

and k = 2π/λ

∴ B = p₀/ks₀

∴ B = 14 × 0.35/(2π × 5.5 × 10⁻⁶)

∴ B = 1.4 × 10⁵ N/m².

Hence, the bulk modulus of the air is 1.4 × 10⁵ N/m².