Question

a sound wave of intensity 300w/m² and frequency π hz.If the density of air is 2kg/m³ and speed of sound in air is 300 m/s. Find the amplitude of sound wave?​

Answer 1

Given:

Intensity of sound wave (I) = 300 W/m²

Frequency of sound wave (f) = π Hz

Density of air (ρ) = 2 kg/m³

Speed of sound in air (v) = 300 m/s

To Find:

Amplitude of sound wave (A)

Answer:

Amplitude of Wave:

$\boxed{ \boxed{ \bf{A = \sqrt{\dfrac{I}{2\pi^2 f^2 \rho v}}}}}$

By substituting values we get:

$\rm \leadsto A = \sqrt{\dfrac{ \cancel{300}}{2\pi^2 \times \pi^2 \times 2 \times \cancel{300}}} \\ \\ \rm \leadsto A = \sqrt{\dfrac{1}{4\pi^4 }} \\ \\ \rm \leadsto A = \dfrac{1}{2\pi^2 } \: m \\ \\ \rm \leadsto A = 0.05 \: m$

$\therefore$ Amplitude of sound wave (A) = $\sf \dfrac{1}{2\pi^2} \ m$ or 0.05 m

Answer 2

I = 2π²f²A²ρv

​300 = 2π²×π²×A××2×300

A = 1/2π²