The intensity of the sound wave

[hidemi]

Homework Statement

The speed of sound in air in 340 m/s, and the density of air is 1.2 kg/m^3. if the displacement amplitude of a 440 Hz sound wave is 10μm. what is the intensity of the wave?

Ans: 32 W/m^2

Relevant Equations

I = 1/2 ρvR²w²

I = 1/2 ρvR²w²

I = 1/2 *1.2kg/m³*340m/s*(10 x 10^-6m)²*(2π*440/s)²

I = 0.16 W/m²

This is my answer which does not match the given answer. Am I doing wrong?

 

[haruspex]

32W/m² is hearing damage in a matter of seconds. Even 0.16 for 30 min is ill-advised.
From a rough calculation, I agree with your answer.