All Problems

Elastic Waves. Acoustics.

Problem 4.159

A point isotropic source generates sound oscillations with frequency v=1.45kHzv=1.45 \mathrm{kHz}. At a distance r0=5.0 mr_{0}=5.0 \mathrm{~m} from the source the displacement amplitude of particles of the medium is equal to a0=50μm,a_{0}=50 \mu \mathrm{m}, and at the point AA located at a distance r=10.0 mr=10.0 \mathrm{~m} from the source the displacement amplitude is η=3.0\eta=3.0 times less than a0.a_{0} . Find: (a) the damping coefficient γ\gamma of the wave; (b) the velocity oscillation amplitude of particles of the medium at the point AA.

Reveal Answer
(a) γ=ln(ηr0/r)rr0=0.08 m1\gamma=\frac{\ln \left(\eta r_{0} / r\right)}{r-r_{0}}=0.08 \mathrm{~m}^{-1} (b) vm=2πva0η=15 cm/sv_{m}=\frac{2 \pi v a_{0}}{\eta}=15 \mathrm{~cm} / \mathrm{s}