All Problems Elastic Waves. Acoustics.
Problem 4.159
A point isotropic source generates sound oscillations with frequency \(v=1.45 \mathrm{kHz}\). At a distance \(r_{0}=5.0 \mathrm{~m}\) from the source the displacement amplitude of particles of the medium is equal to \(a_{0}=50 \mu \mathrm{m},\) and at the point \(A\) located at a distance \(r=10.0 \mathrm{~m}\) from the source the displacement amplitude is \(\eta=3.0\) times less than \(a_{0} .\) Find: (a) the damping coefficient \(\gamma\) of the wave; (b) the velocity oscillation amplitude of particles of the medium at the point \(A\).
(a) \(\gamma=\frac{\ln \left(\eta r_{0} / r\right)}{r-r_{0}}=0.08 \mathrm{~m}^{-1}\) (b) \(v_{m}=\frac{2 \pi v a_{0}}{\eta}=15 \mathrm{~cm} / \mathrm{s}\)