Question

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 m, the radius of the ring is R = 0.50 m. Find the mean energy flow across the area enclosed by the ring if at the point 0 the intensity of sound is equal to I₀ = 30 μW/m². The damping of the waves is negligible.

Answer 1

The power output of the source much be

The required flux of accoustic power is then : 

Where Ω is the solid angle subtended by the disc enclosed by the ring at S. This solid angle is

Eqn. (1) is a well known result stich is derived as follows; Let SO be the polar axis. Then the required solid angle is the area of that part of the surface a sphere of much radius whose colatitude is ≤ α.

Thus