Ultrasound Attenuation
Even when no single boundary reflects the whole pulse, the beam becomes weaker as it travels through matter. This gradual loss is attenuation.
Equal extra thickness multiplies intensity
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Absorption and scattering transfer energy away from the useful beam. The transmitted intensity therefore falls exponentially, not by the same number of watts for every added centimetre.
Symbols
- = transmitted intensity after thickness x (W m⁻²)
- = incident intensity (W m⁻²)
- = linear attenuation coefficient (m⁻¹ or cm⁻¹)
- = distance through the material (m or cm)
Key idea
The product must have no unit. If the coefficient is in cm−1, use centimetres for the thickness.
Worked example
Intensity after tissue attenuation
A beam of initial intensity 8.0 W m−2 travels through 3.0 cm of tissue with an attenuation coefficient of 0.20 cm−1.
Answer
Your turnnumerical check
A beam passes through 5.0 cm of material with μ = 0.14 cm−1. Find the fraction of the initial intensity that remains.
Show worked answer
About 0.50, or 50%, of the incident intensity remains.
Common mistake
Attenuation is the gradual reduction of the beam as it travels. Reflection is the change at a boundary. A question may involve both.