How do I find the equivalent two-way beam angle Ψ for my Echosounder?

The Equivalent two-way beam angle (TWBA) \(\Psi\) is frequency and transducer-specific, and the value can be calculated (in Steradians) for the circular transducer through the following equation (for \(ka\)>10):

 

\( \Psi = \frac {5.78}{(k a)^2} \)(1)
  
or in dB format: 
  
\( EBA = 10 log (\Psi) \)(2)
    
 \(k\)-wave number \( k= \frac{2 \pi}{\lambda}\)
 \( \lambda\)-wavelength \( [m]\)
 \(a\)-active radius of the transducer \( [m]\)

 

The calculated Equivalent two-way beam angle for each instrument with monochromatic setup is given in the table below:

 

Instrument/Frequency
[mm]
Ψ
[sr]
Ψ
[dB]
Signature 1000150.0015-28.3443
Signature 500300.0015-28.3443
Signature 250/500kHz 408.23e-04-30.8431
Signature 100/70kHz43.50.0355-14.4942
Signature 100/90kHz43.50.0215-16.6771
Signature 100/120kHz43.50.0121-19.1759

Updated