Chapter 13. Sound wave intensity in terms of pressure amplitude Pmax (13-31)

Review

Equation 13-29 is expressed in terms of the displacement amplitude A. However, our ears are more directly sensitive to the pressure variations in a sound wave. The displacement amplitude A in a sound wave is related to the pressure amplitude pmax, or maximum pressure variation, by

(13-30) \(A = \frac{p_{\mathrm{max}}}{\rho{v_{\mathrm{sound}}}\omega}\)

If we substitute Equation 13-30 for \(A\) into Equation 13-29, we get an alternative expression for the intensity of a sound wave:

\(I = \frac{1}{2}\rho{v_{\mathrm{sound}}\omega^2}\left(\frac{p_{\mathrm{max}}}{\rho{v_{\mathrm{sound}}}\omega}\right)^2 = \frac{p_{\mathrm{max}}^2}{2}\frac{\rho{v_{\mathrm{sound}}}\omega^2}{\rho^2v_{\mathrm{sound}}^2\omega^2}\)

or, simplifying,