All Problems

Elastic Waves. Acoustics.

Problem 4.181

Find the damping coefficient γ\gamma of a sound wave if at distances r1=10 mr_{1}=10 \mathrm{~m} and r2=20 mr_{2}=20 \mathrm{~m} from a point isotropic source of sound the sound wave intensity values differ by a factor η=4.5\eta=4.5.

Reveal Answer
γ=ln(ηr12/r22)2(r2r1)=6103 m1\gamma=\frac{\ln \left(\eta r_{1}^{2} / r_{2}^{2}\right)}{2\left(r_{2}-r_{1}\right)}=6 \cdot 10^{-3} \mathrm{~m}^{-1}