The specific forced radiation wave impedance of a finite rectangular panel excited by a plane sound wave

The average specific forced radiation wave impedance of a finite rectangular panel, excited by a plane sound wave incident at a particular angle of incidence, is of importance for the prediction of both sound insulation and sound absorption. In 1982, Thomasson published numerical calculations of the average specific forced radiation wave impedance of a square of side length 2e for wave number k for values of ke in half octave steps from 0.25 to 64. Thomasson also published approximate formulae for values of ke above and below the published results. This paper combines Thomasson's high and low frequency formulae and compares this combined formula with Thomasson's numerical calculations. The real part of the approximate formula is between 0.7 dB higher and -1 dB lower than the numerical calculations. The imaginary part of the approximate formula is between 2.3 dB higher and - 2.6 dB lower than the numerical calculations. These extreme differences occur in the region of ke equals 2. However the imaginary part also has a difference of 1.7 dB for ke equals 64 at an angle of incidence of the forcing wave of 60 degrees relative to the normal to the square panel. An approximate formula for the real part developed previously by Davy is between 0.4 dB higher and -0.6 dB lower than Thomasson's numerical calculations. Thus it is in slightly better agreement with Thomasson's numerical calculations than the formula obtained by combining Thomasson's high and low frequency approximations. The imaginary specific radiation impedance of a rigid disk of equal area to a square and vibrating in phase gives a good approximation, up to ke equals 5, to the imaginary part of the specific forced radiation impedance of a square which has been excited by a plane wave incident normally to the square.