Question

The maximum variation in pressure P that ear can tolerate in loud sound is about 28 N/m² What iap the corresponding maximum displacement for a sound of frequency 500Hz in air? Density of air is 1.22kg/m^{3 and velocity of sound is 330m/s}

Answer 1

$$\begin{gathered} Theformulaformaximumpressurevariation∆Pwhichrelates \\ maximumdisplacement{S}_m,soundfrequency\upsilon ,density\rho andvelocityvofsoundinairisgiven: \\ ∆P=v\rho \omega \times S_m \\ So{S}_m=\frac{∆P}{v\rho \omega } \\ or{S}_m=\frac{28}{330\times 1.22\times 2\pi \times 500} \\ or{S}_m=\frac{28}{330\times 1.22\times 2\times 3.14\times 500} \\ or{S}_m=0.000022m=2.2\times {10}^{-5}m \end{gathered}$$