Ultrasound enters tissue with I₀ = 200 W m⁻² and intensity attenuation coefficient μ = 15 m⁻¹. A reflecting interface lies 4.0 cm deep with intensity reflection coefficient 0.040. Neglect spreading and coupling losses. Calculate intensity incident on the interface and the echo intensity at the entrance. Explain why using x = 0.040 m just once, or omitting the reflection coefficient, gives the wrong echo result.

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Interface incident intensity ≈ 110 W m⁻²; entrance echo ≈ 2.41 W m⁻². The echo travels 0.080 m in tissue and only 4% is reflected. d = 0.040 m and μd = 0.60. I_interface = 200e^(−0.60) = 109.8 W m⁻². I_echo = 200 × 0.040 × e^[−15(2 × 0.040)] = 2.41 W m⁻². Using one passage omits the return attenuation; omitting 0.040 assumes 100% reflection. The calculation uses intensity coefficients and assumes no additional losses.

Account for both propagation paths and reflection

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