What is the Amplitude of eardrum vibrations at this intensity?

Question

The eardrum is displaced surprisingly little when a sound wave strikes it. Some idea of the displacement of the eardrum by a sound wave can be obtained by using: I = 2pi^2(wave speed)(1.3kg/m^3)(Frequency^2)(A^2)

The displacement amplitude, A, of the air molecules gives us a lower limit to the displacement of the eardrum. The threshold of pain begins at an intensity of 1 0W m2 [19]. What is the amplitude of eardrum vibrations at this intensity?

____?___10^3nm (at threshold of pain)

Answer 1

Just solve the equation you're given, and pick appropriate values for frequency and wave speed (sound velocity).

if  I = 2pi^2(wave speed)(1.3kg/m^3)(Frequency^2)(A^2), then

A = sqrt[I / {2pi^2(wave speed)(1.3kg/m^3)(Frequency^2)}]