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Elastic Waves. Acoustics.

Problem 4.181

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

Reveal Answer
γ=ln⁡(ηr12/r22)2(r2−r1)=6⋅10−3 m−1\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}
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