Medical Imaging Systems · Ultrasound Imaging · 2 marks · Numerical answer
A circular ultrasound transducer has radius a=8 mm,frequency 1 MHz,and axial pressure $P(r,0)\propto\sin(ka^2/(4r))$. Sound speed is 1600 m/s. Find positive intensity reduction from r=8 cm to 16 cm in dB, to two decimals.
The wavenumber is k=2πf/c. The sine arguments at eight and sixteen centimetres are π/4 and π/8 respectively. Intensity is proportional to pressure squared, so reduction is $20\log_{10}[\sin(\pi/4)/\sin(\pi/8)]\approx5.33$ dB. Using ten times the logarithm of the pressure ratio would miss the square.
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