An accelerometer shows how one tank location moves. Sound power depends on the motion of the radiating surface and the surrounding acoustic field. Two panels with the same measured local velocity can therefore produce different acoustic outputs.
Even equal area-averaged mean-square normal velocity does not settle the comparison. A panel whose regions move together can reinforce radiation. Alternating regions can partly cancel, with the result depending on frequency, panel dimensions and receiver direction.
Define the efficiency you are using
For a surface area S in square metres, define an equivalent radiation efficiency σ by W = ρcSσ〈vₙ,rms²〉. Here W is radiated power in watts, ρ is fluid density in kilograms per cubic metre, c is sound speed in metres per second, and the bracket denotes an area average of squared RMS normal velocity.
This equation defines σ for the stated surface, frequency and acoustic conditions. It does not supply its value. If two panel regions interact acoustically, assigning independent efficiencies and adding their powers may omit their cross terms.
| Measured or modeled feature | Why it changes the acoustic interpretation |
|---|---|
| Normal velocity distribution | Tangential motion alone does not describe boundary radiation |
| Relative phase across the panel | Controls reinforcement and cancellation |
| Panel dimensions relative to wavelength | Affects directional radiation and spatial averaging |
| Nearby surfaces and boundaries | Change the acoustic transfer and reflected field |
| Frequency and mode shape | Change the pattern even at equal velocity magnitude |
Compare structural and acoustic spatial scales
The acoustic wavenumber is k = ω/c in radians per metre. A structural mode has its own spatial variation. When panel motion changes sign rapidly over distances small compared with the acoustic wavelength, neighboring contributions may cancel strongly in some directions.
That qualitative comparison is not a universal efficiency formula. Finite boundaries, stiffeners, edges and curved surfaces alter radiation. An ideal infinite-plate argument should not be transferred directly to a transformer tank.
Measure enough surface points to resolve the relevant mode shape and phase. A sensor placed at a modal node can understate motion; one at an antinode can overstate the average. Use a common phase reference and retain normal directions when combining measurements from different faces.
Check a proposed panel change at the acoustic output
A stiffener can reduce local velocity while changing the mode pattern elsewhere. A damping treatment can affect one resonance more than neighboring frequencies. Evaluate the surface response and the corresponding radiated field over the operating band rather than accepting a single-point reduction as a noise result.
Where practical, compare predicted power with an appropriately qualified acoustic measurement under the same operating and boundary conditions. Keep tonal bands separate from background and auxiliary sources. The analysis should explain which surface motion radiates efficiently and which largely cancels. That information is more useful for selecting a tank modification than an isolated velocity number.
Compare two radiation efficiencies at identical surface velocity
Assume 100 Hz radiation into air with ρ = 1.20 kg/m³, c = 343 m/s, radiating area 2.0 m² and area-averaged RMS normal velocity 1.0 mm/s. If two surface patterns have assumed radiation efficiencies of 0.10 and 0.40, W = ρcSσ〈v²〉 gives 82.32 and 329.28 μW. The power ratio is 4, corresponding to 10 log₁₀4 = 6.02 dB despite identical velocity level. Obtain the efficiencies from the defined acoustic field or a qualified measurement; one accelerometer cannot determine which pattern applies [1][2]. Judge the acoustic outcome using defined transformer and cooling-device sound conditions [1].
References
- IEC, IEC 60076-10:2016, Power transformers – Part 10: Determination of sound levels, 2016, official public scope.
- COMSOL AB, Acoustics Module User’s Guide: The Pressure Acoustics, Boundary Elements Interface, version 6.3.