Question

A point isotropic source generates sound oscillations with frequency v = 1.45 kHz. At a distance r₀ = 5.0 m from the source the displacement amplitude of particles of the medium is equal to a₀ = 50 μm, and at the point A located at a distance r = 10.0 m from the source the displacement amplitude is η = 3.0 times less than a₀. Find: 

(a) the damping coefficient γ of the wave; 

(b) the velocity oscillation amplitude of particles of the medium at the point A.

Answer 1

(a) We know that the equation of a spherical wave in a homogeneous absorbing medium of wave damping coefficient γ is :

Thus particle’s displacement amplitude equals

According to the conditions of the problem,