Attenuation coefficient from backwall echoes

Sound loses amplitude as it travels through a material by absorption and by scattering off the grain structure. The loss is exponential with distance and is quoted as an attenuation coefficient in dB per mm of sound path. It is measured on a parallel-sided piece by comparing two successive backwall echoes: the second has travelled a longer path by exactly the difference in the two path lengths, and the extra loss over that distance gives the coefficient.

The raw amplitude difference is not all attenuation. In the far field the beam also spreads, so a plane backwall reflector at twice the distance returns less signal even in a lossless material — by 20·log₁₀(z₂/z₁), which is 6.02 dB when the second echo is at twice the path. That geometric term must be subtracted before the remainder is called attenuation. Leaving it in is the most common error in this measurement and inflates the answer badly on thin sections.

Attenuation rises steeply with frequency, so the coefficient is meaningless unless the frequency is recorded with it. Expressing the result in dB per wavelength makes results at different frequencies comparable and is the honest way to compare, say, a fine-grained forging with a coarse austenitic casting. Typical fine-grained ferritic steel at 4–5 MHz gives well under 0.02 dB/mm; a coarse-grained austenitic weld or casting can be an order of magnitude worse and may simply be uninspectable at that frequency.

The measurement only holds if both echoes lie in the far field, the surfaces are parallel and equally coupled, and neither echo is clipped or in the instrument's non-linear range. Attenuation measured this way is 'apparent' attenuation — it includes couplant and surface losses at each reflection and is not a pure material constant.

Path to echo n:  zₙ = 2 · n · t
Beam-spread term = 20 · log₁₀( z₂ / z₁ )
α = ( ΔdB − beam spread ) / ( z₂ − z₁ )
α per wavelength = α · λ