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 OO of the ring. The distance between the point OO and the source is l=1.00 m,l=1.00 \mathrm{~m}, the radius of the ring is R=0.50 m.R=0.50 \mathrm{~m} . Find the mean energy flow across the area enclosed by the ring if at the point OO the intensity of sound is equal to I0=30μW/m2I_{0}=30 \mu \mathrm{W} / \mathrm{m}^{2}. The damping of the waves is negligible.

Reveal Answer
Φ=2πl2I0(111+(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}