| Popis: |
Eckart’s equation in the presence of the volume source density q is ⧠2[π+2(Ψ2),00]=ΓV,00−ρ0c0q,0. The interaction terms [(ρ0−ρ)c0q,0−qc0ρ,0] are absent, a consequence of ⧠2ρs=−ρ0c0q,0. If the approximate first‐order solution for a radiator with directivity D1(ω,θ,φ), p1=P0r0|r′|−1D1[cos(ωt−kr+Ψ)]exp[ −rα(ω)] in which r′=r0+ir, r0=Rayleigh distance, Ψ=arctan(rr0−1), P0=ρoc0u0 with piston velocity u0, is introduced into Eckart’s equation the second‐order pressure is obtained: p2=Γ(4ρ0c20)−1P20D21kr20|r′&u|−1[(ln|r′|r0−1)2+Ψ2]1/2[cos( 2ωt−2kr+Ψ−χ)]exp[−2rα(ω)] in which χ=arctan[Ψ(ln|r′|r0−1)−1]. Matching solutions at r=r0 yields the term generating fingers: pf=P*r0r−1D2[cos(2ωt−2kr+1/4π−δ)]exp[(r 0 −r)α(2ω)−2r0α(ω)] in which δ=arctan[1/4π(ln√2)−1], D2=D(2ω,θ,φ), and P*=Γ(4ρ0c20)−1P20kr02−1/2[(ln√2 )2+(1/4π)2]1/2. For rectangular radiators the zero’s of D1 coincide with the zero’s of D2 therefore fingers do not occur in the case. The total pressure pt=p2+pf. Fingers arise from colinear interaction and have no... |
