The eardrum is displaced surprisingly little when a sound wave strikes it. Some

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 Equation 7.1: The displacement amplitude, A, of the air molecules gives us a lower limit to the displacement of the eardrum. At the threshold of hearing at 3.2 kHz, the sound intensity is about 10-12W/m2. The threshold of pain begins at an intensity of 1.0W/m2 [19]. What is the amplitude of eardrum vibrations at these intensities? The density of air is 1.3kg/m3 [19] F. R. Hallett, P. A. Speight, R. H. Stinson, INTRODUCTORY BIOPHYSICS, (New York: John Wiley & Sons, 1977). 10~3nm (at threshold of 3.39 hearing) (This value is ~3/100 the diameter of a hydrogen atom!) 3390 10'nm (at threshold of pain)

Explanation / Answer

Solving the goven eqn for A we get

A = sqrt (I/2 pi^2 v rho f^2)

A = sqrt (10^-12/(2 x 3.14^2 x 343 x 1.3 x 3200^2) = 3.333 x 10^-12 m

Hence, A = 3.33 x 10^-3 nm

For I = 1 W/m^2

A = sqrt (1/(2 x 3.14^2 x 343 x 1.3 x 3200^2) = 3.333 x 10^-6 m

A = 3.333 x 10^-6 m

A = 3333 nm

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.