The attenuation coefficient (symbol α) describes how quickly an ultrasonic wave loses energy as it travels through a medium. Where acoustic impedance is read from a reflection at one boundary, attenuation is read across a transmission path — which changes both what it is good at and how it fails.
Definition
Pressure amplitude decays exponentially with distance:
A(x) = A₀ e−αx
where x is path length. α is expressed in nepers per metre (Np/m) or, more commonly in industry, decibels per metre (dB/m). The conversion is 1 Np/m = 8.686 dB/m.
Two mechanisms, not one
Total attenuation is the sum of two physically distinct effects, and the distinction is what makes the method useful:
- Absorption converts acoustic energy to heat through viscous and thermal losses in the fluid. It is a property of the carrier liquid and rises with frequency.
- Scattering redirects energy away from the receiver when the wave meets suspended particles. It depends on particle concentration, particle size relative to wavelength, and the density and compressibility contrast between particle and liquid.
In a slurry the scattering term dominates and rises monotonically with solids concentration over a wide range. That monotonic relationship is what a transmission-type ultrasonic meter such as the PS7010 calibrates against.
Why frequency and particle size matter
Scattering behaviour splits by the ratio of particle size d to acoustic wavelength λ:
- d « λ (Rayleigh regime): scattering rises very steeply with frequency. Fine particles are nearly invisible at low frequency.
- d ≈ λ: the transition region, where the response is strongest and also most sensitive to a shift in the particle size distribution.
- d » λ: geometric regime, where scattering flattens out and depends mainly on projected area.
The practical consequence is one every user should know: an attenuation-based calibration is tied to the particle size distribution it was made on. If the grind changes materially — a new ore body, a mill upset, a screen change — the concentration reading can shift even though the mass concentration has not. This is not a defect; it is the physics. It is also why the method is normally calibrated against the actual process liquid rather than against a reference fluid.
Why bubbles are worse here than anywhere else
Gas bubbles both scatter strongly and resonate. Near resonance a bubble presents an acoustic cross-section far larger than its geometric size, so a void fraction of well under one percent can absorb the transmission path entirely and drive the received signal toward zero. This is why through-transmission instruments specify low-bubble service, and why a degassing point or a location under static head is chosen when there is a choice.
Path length is a design decision
Received energy falls exponentially with path length, so pipe diameter is not a free parameter. Too short a path and the concentration resolution suffers because the signal barely changes; too long and the received signal falls into the noise at high concentration. This is the reason a transmission instrument carries a bounded diameter range — DN50 to DN500 for the PS7010 — while a reflection instrument does not.
When to choose attenuation over impedance
| Situation | Better fit |
|---|---|
| Cannot tap the pipe / no shutdown window | Attenuation (clamp-on) |
| Large diameter, above DN500 | Impedance |
| Known entrained gas | Impedance |
| Variable, unpredictable grind | Impedance |
| Lined or non-metallic pipe | Depends on wall — ask before ordering |
| Temporary or trial installation | Attenuation (clamp-on) |
The clamp-on advantage is real and often decisive: no tapping, no process interruption, and the instrument can be relocated if the first position turns out to be wrong. That last point matters more than it sounds, because installation position is the most common cause of a disappointing first week.