MECH7029 Chap.5 Monopole, Dipole and Quadrupole Sources
Monopole, Dipole and Quadrupole Sources
Classify mechanisms, not machines
Elementary source types follow from how the source-free wave assumptions are disturbed. Changing volume flow produces monopole-like radiation, unsteady force produces a dipole, and nonlinear stress in free flow is represented by quadrupoles. Directivity and cancellation check the label.
Finite bodies, vents, enclosures and nearby surfaces mix the ideals, so one product may contain several source classes.
Symmetry determines cancellation
A compact monopole sends the same pressure sign outward at a given instant and has no intrinsic directional null. A dipole combines nearby opposite sources, so equal paths cancel in the plane perpendicular to its force axis.
Pairing dipoles creates a quadrupole with stronger spatial cancellation. These patterns are limiting descriptions; source size must be small compared with wavelength before their simple lobes are expected.
The hierarchy also explains low-Mach efficiency. Each additional cancelling partner suppresses far-field radiation more strongly as characteristic source speed falls.
That trend does not mean every monopole is louder than every dipole, because source strength, frequency, size and boundaries remain different.
It predicts how comparable mechanisms may change relative importance during a controlled speed sweep.
Boundaries turn one machine into a mixture
A vent carries oscillating volume flow, a vibrating casing applies force to the air, free turbulence contributes nonlinear stress, and a stationary edge can interrupt cancellation to expose a surface-force term.
The machine name supplies none of those classifications by itself. A good diagnosis identifies the varying physical quantity, predicts a null or lobe, and then states how finite size or a nearby surface could alter the compact ideal.
What this chapter covers
- 01
Volume-flow monopoles
- 02
Force-source dipoles
- 03
Turbulent-stress quadrupoles
- 04
Compact-source directivity
- 05
Finite-size cancellation errors
- 06
Vehicle and machinery source mixtures
Worked example · free
Decompose a machine into source mechanisms
- 3Classify changing volume at the vent.
- 4Classify casing force and free-jet stress.
- 2Use a null direction to test one classification.
Key terms
- Monopole Source
- A compact source created by fluctuating volume flow.
- Dipole Source
- A compact source created by fluctuating force.
- Quadrupole Source
- A paired force pattern representing nonlinear stress radiation.
- Directivity
- The variation of radiated amplitude with observer direction.
- Compact Source
- A source whose dimensions are small relative to acoustic wavelength.
Monopole, Dipole and Quadrupole Sources FAQ
Does structural vibration always create only dipole sound?
A compact rigid body vibrating at nearly constant volume is dipole-like, but finite size and unequal path lengths weaken cancellation and leave monopole-like content. Enclosures, openings and attached surfaces can add separate mechanisms as well.
Why is a monopole generally efficient at low Mach number?
Its field lacks the opposed spatial partner that cancels dipole and quadrupole radiation. Higher multipoles contain additional cancellation and stronger Mach-number dependence, so their power falls more rapidly as source speed becomes small.
Can a stationary solid edge radiate aerodynamic sound?
The edge need not move. It can break the symmetry of turbulent pressure structures and prevent cancellation, exposing a fluctuating surface-force contribution with dipole character. Trailing-edge scattering is an important example.
Exam move
Build a source-classification notebook around mechanisms rather than products. Select five systems such as a loudspeaker box, fan, jet, vibrating panel and vented enclosure. For each, list every region where volume flow, applied force or internal stress varies. Assign an elementary source only after writing that physical cause.
Draw the compact directivity, label the expected nulls, and compare source dimension with wavelength to decide whether the simple pattern is plausible. Add one boundary correction to every sketch: an enclosure hiding a rear field, an edge breaking cancellation, a moving surface changing observer geometry, or unequal path lengths exposing a residual component.
Then rank how each ideal power might change with Mach number without claiming that the scaling coefficient is the same. Practise short answers that begin with a conservation statement and end with a discriminating observation. For example, a side null supports a dipole axis, while nearly uniform radiation supports a compact monopole but does not prove it uniquely.
Repeat one example at a shorter wavelength and explain why non-compact phase differences complicate the lobes. Finish by decomposing a complete machine into simultaneous vent, casing, surface-loading and turbulence contributions. If an answer contains only one label, inspect whether a mechanism has been overlooked. Keep a correction table for cause, cancellation, directivity, compactness and boundary effect.
During final review, cover the labels on each lobe sketch and recover the source class from symmetry alone, then uncover the mechanism statement to verify that visual and conservation arguments agree.
