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GATE 2021 BM – Question 51

Medical Imaging Systems · Ultrasound Imaging · 2 marks · Multiple choice

A longitudinal ultrasound wave meets a muscle–kidney boundary at 60°. Acoustic impedances are 1.70×10⁵ and 1.62×10⁵ g cm⁻² s⁻¹; sound speeds are 1590 and 1560 m/s respectively. Transducer frequency is 1.5 MHz. Find transmitted angle in degrees (nearest integer) and intensity transmission coefficient (two decimals).

  1. 58,0.24
  2. 30,0.68
  3. 58,0.94
  4. 30,0.99

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Correct answer: (C) 58,0.94

Explanation

Snell’s law gives sinθt=(1560/1590)sin60°, so θt≈58.2°, rounded fifty-eight. For pressure transmission tp=2Z₂cosθi/(Z₂cosθi+Z₁cosθt). The transmitted-to-incident ray-intensity ratio is (Z₁/Z₂)tp²≈.94. Thus C. Multiplying this ratio by cosθt/cosθi instead gives the normal energy-flux coefficient, a different quantity.

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