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GATE 2023 BM – Question 45

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

An ultrasonic wave of incident pressure amplitude P₀ strikes a boundary normally from acoustic impedance Z₁ toward Z₂. What is the total pressure amplitude at the boundary on the incident side?

  1. $2P_0Z_2/(Z_1+Z_2)$
  2. $P_0(Z_2-Z_1)/(Z_1+Z_2)$
  3. $P_0Z_2/Z_1$
  4. $P_0Z_1/(Z_1+Z_2)$

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Show answer and explanation

Correct answer: (A) $2P_0Z_2/(Z_1+Z_2)$

Explanation

The pressure reflection coefficient is r=(Z₂−Z₁)/(Z₂+Z₁). At the boundary the incident and reflected pressures add, giving P₀(1+r)=P₀[(Z₁+Z₂+Z₂−Z₁)/(Z₁+Z₂)]=2P₀Z₂/(Z₁+Z₂). This matches A; B gives the reflected component alone.

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