All Problems

Elastic Waves. Acoustics.

Problem 4.162

A point isotropic sound source is located on the perpendicular to the plane of a ring drawn through the centre \(O\) of the ring. The distance between the point \(O\) and the source is \(l=1.00 \mathrm{~m},\) the radius of the ring is \(R=0.50 \mathrm{~m} .\) Find the mean energy flow across the area enclosed by the ring if at the point \(O\) the intensity of sound is equal to \(I_{0}=30 \mu \mathrm{W} / \mathrm{m}^{2}\). The damping of the waves is negligible.

Reveal Answer
⟨Φ⟩=2πl2I0(1−11+(R/l)2)=20μW\langle\Phi\rangle=2 \pi l^{2} I_{0}\left(1-\frac{1}{\sqrt{1+(R / l)^{2}}}\right)=20 \mu \mathrm{W}
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