MECH7029 Aeroacoustics and Noise Control with Machine Learning
The Complete Exam Bible · First Semester, 2026-27MECH7029 Overview
- The University of Hong Kong
- First Semester, 2026-27
- Postgraduate engineering
- Mathematical acoustics and noise control
What this course asks you to connect
MECH7029 treats acoustics as oscillatory compressible flow and noise control as a matching problem.
- Assessment Continuous assessment, including a mid-term quiz, carries 50%; the final exam carries 50%.
- Core method Name the wave or source model, state its assumptions, compute in linear quantities, then test a limit.
- Design warning Every tuned control needs an off-design check for a passband, frequency drift or narrow bandwidth.
- Coverage The detailed captured teaching materials support sound levels, aeroacoustic sources and duct acoustics.
How MECH7029 is assessed
| Component | Weight | Format |
|---|---|---|
| Continuous assessment | 50% | Includes a mid-term quiz; captured Moodle pages also show Chapter 1 and Chapter 2 submissions |
| Final exam | 50% | The captured files publish the weight but not the duration, sections, question count or permitted materials |
The Moodle course arrangement and instructor cover material publish the same split: continuous assessment, inclusive of a mid-term quiz, is 50%, and the final exam is 50%. The captured files do not divide the continuous-assessment share further or state the final-exam duration, sections, question count or permitted materials. Check Moodle when those operational details are published.
Assessment structure
Current MECH7029 dates
| Date | Item | Control |
|---|---|---|
| 23 September 2026 | Chapter 1 assignment | Due at 10:00 PM on the captured Moodle assignment page. |
| 30 September 2026 | Chapter 2 assignment | Due at 10:00 PM on the captured Moodle assignment page. |
Dates are as published in the captured Moodle assignment pages for this offering. Confirm exact deadlines and submission settings in the live LMS.
What MECH7029 covers
Nine grounded chapters move from sound levels and measurement through wave mechanics and aeroacoustic sources to duct modes, expansion chambers and tuned resonators.
Sound Waves, Pressure Levels and Energy
RMS pressure, logarithmic levels, acoustic intensity and the distinction between wave speed and particle motionPressure is not particle travel
This chapter separates the pressure pattern moving through air from the small oscillation of the particles that carry it.
- Travelling-wave phase and wavenumber
- Peak and root-mean-square pressure
- Sound pressure level and the reference pressure
- Acoustic intensity and power
- Pressure doubling and level change
- Wave speed against particle velocity
Frequency Bands, Weighting and Level Addition
octave ratios, spectra, A-weighting, energetic addition and background subtractionSpectra decide what can be controlled
This chapter organises the audible range into octave and one-third-octave ratios, then explains how a time signal becomes a spectrum.
- Octave and one-third-octave bands
- Geometric centre frequency
- Tone, impulse and broadband spectra
- A-weighting by frequency band
- Energetic addition of independent levels
- Background subtraction in linear units
Hearing, Measurement and Noise Descriptors
ear response, microphone choice, calibration, equivalent level and percentile descriptorsThe descriptor belongs to a question
This chapter follows sound through the ear and through a measurement chain. Microphone type, orientation, calibration and field geometry define the evidence before a digital value appears.
- Outer, middle and inner ear roles
- Frequency-dependent hearing response
- Sound-level-meter signal chain
- Microphone type and directional response
- Calibration before and after measurement
- Equivalent and percentile noise levels
Wave Equation and Acoustic State Relations
mass and momentum conservation, isentropic closure, sound speed and travelling-wave impedancePropagation emerges from three balances
The homogeneous wave equation is derived from linearised mass conservation, momentum conservation and isentropic thermodynamics.
- Ideal-gas and isentropic relations
- Linearised mass conservation
- Linearised momentum conservation
- One-dimensional wave equation
- Travelling-wave pressure and velocity
- Sound speed and particle displacement
Monopole, Dipole and Quadrupole Sources
volume, force and stress mechanisms with directivity, cancellation and finite-size correctionsClassify mechanisms, not machines
Elementary source types follow from how the source-free wave assumptions are disturbed.
- Volume-flow monopoles
- Force-source dipoles
- Turbulent-stress quadrupoles
- Compact-source directivity
- Finite-size cancellation errors
- Vehicle and machinery source mixtures
Acoustic Analogy, Power Laws and Fan Noise
Lighthill stress, Mach scaling, moving surfaces, broadband mechanisms and blade-passing ordersUse the spectrum as a mechanism test
Lighthill's acoustic analogy places nonlinear flow terms on the right-hand side of a familiar wave operator.
- Lighthill stress tensor
- Equivalent source interpretation
- Mach-number power laws
- Moving-boundary terms
- Broadband fan mechanisms
- Blade-passing frequency and orders
Standing Waves, Junctions and Duct Modes
reflection phase, continuity at area changes, higher-mode cut-on and open-end correctionMatch fields at boundaries
A duct field is a superposition of waves, so reflection creates pressure and particle-velocity patterns with different node positions. At an area change, acoustic pressure and volume flow must be matched.
- Travelling and reflected waves
- Pressure and velocity nodes
- Area-junction continuity
- Reflection and transmission coefficients
- Higher-mode cut-on
- Open-end correction
Expansion Chambers and Transmission Loss
two-junction interference, area-ratio control, quarter-wave peaks and half-wave passbandsInterference creates both peaks and passbands
An expansion chamber contains two area junctions separated by a propagation length. Its transmission loss therefore depends on both impedance mismatch and phase.
- Two-junction chamber model
- Transmission-loss definition
- Area-ratio mismatch
- Quarter-wave attenuation peaks
- Half-wave passbands
- Plane-wave and lossless assumptions
Quarter-Wave and Helmholtz Resonators
neck inertia, cavity stiffness, effective length, damping, bandwidth and side-branch reflectionTune reactance, then confront bandwidth
A quarter-wave side branch uses distributed propagation, whereas a compact Helmholtz resonator uses neck-air inertia and cavity-air stiffness. Both can create strong reflection near a target frequency.
- Quarter-wave side branches
- Neck acoustic mass
- Cavity acoustic stiffness
- Effective neck length
- Resistance and damping
- Bandwidth and detuning
A useful solution begins with what is measured, identifies how pressure, velocity and energy propagate, locates the physical source, and chooses a control whose frequency response suits that source.
The captured calendar description emphasises sound radiation by structural vibration and flow, with noise reduction as the engineering purpose.
Sound levels and measurement
The opening chapters build the scale used everywhere else. A pressure trace must be converted from peak to root-mean-square amplitude before sound pressure level is formed.
Levels from independent bands or sources combine through linear energy, not by adding decibel labels.
Octave bands and spectra show where energy lies, A-weighting represents frequency-dependent hearing sensitivity, and environmental descriptors such as equivalent and percentile levels answer different time-distribution questions.
From conservation laws to source mechanisms
The wave equation follows from mass conservation, momentum conservation and an isentropic pressure-density relation after small disturbances are linearised.
This derivation is also a source map. Fluctuating volume enters as a monopole, unsteady force as a dipole, and nonlinear turbulent stress as a quadrupole-like distribution. Real machines mix these ideals because boundaries and finite size weaken cancellation.
Aeroacoustics and fan noise
Lighthill's acoustic analogy rearranges the exact flow equations into an equivalent sound-source problem.
Its value lies in separating the analytical propagation operator from source terms that can be approximated.
The course then uses Mach-number power laws, broadband and discrete spectra, moving-surface terms and blade-passing frequency to connect a measured fan spectrum with plausible physical mechanisms.
Duct fields and control devices
Opposing waves form standing fields whose pressure and velocity maxima occupy different positions.
Area changes require pressure and volume-flow continuity, while duct geometry sets higher-mode cut-on frequencies. Expansion chambers exploit reflection and phase interference, producing quarter-wave peaks and half-wave passbands.
Quarter-wave and Helmholtz side branches create tuned reflection; the Helmholtz device uses neck inertia, cavity stiffness and resistance.
How to revise with this guide
Work each chapter's original calculation without looking at the response. Follow it with the limiting-case question: pressure doubled, frequency moved, area ratio increased, mode below cut-on or resonator driven off resonance.
The most valuable final sentence states what the number means physically and which changed fact would require another model. Use Moodle for later course materials and for final assessment details when the University publishes them.
Worked example · free
Tune a compact resonator and test its weak point
- 3Calculate neck area and effective length including virtual mass.
- 4Rearrange the resonance formula and compute cavity volume.
- 3Explain the off-resonance bandwidth risk and the role of damping.
Key terms
- Root Mean Square
- The square root of the time average of squared pressure, used because acoustic energy depends on squared amplitude.
- Sound Pressure Level
- A logarithmic measure of RMS sound pressure relative to the airborne reference pressure.
- Octave Band
- A frequency band whose upper edge is twice its lower edge, with a geometric centre frequency.
- A-weighting
- A frequency-dependent correction applied to band levels before energetic addition to represent hearing sensitivity.
- Percentile Level
- A level exceeded for a stated percentage of a stated measurement duration.
- Characteristic Impedance
- The product of mean density and sound speed linking pressure and particle velocity in a travelling plane wave.
- Monopole Source
- A compact fluctuating volume-flow source with approximately uniform directivity.
- Dipole Source
- A compact fluctuating-force source with opposed lobes and a null perpendicular to its axis.
- Acoustic Analogy
- A rearrangement of the exact flow equations into a wave operator driven by equivalent source terms.
- Blade-Passing Frequency
- The product of blade count and rotational frequency, marking the primary periodic passage order.
- Cut-on Frequency
- The threshold above which a duct mode has a real axial wavenumber and can propagate.
- Transmission Loss
- Ten times the logarithm of incident to transmitted acoustic power for a defined element and wave condition.
- Helmholtz Resonator
- A compact tuned cavity in which neck-air inertia interacts with cavity-air stiffness and damping.
MECH7029 FAQ
How is the course assessed?
The published split has two equal halves. Continuous assessment, explicitly including a mid-term quiz, carries fifty percent, and the final exam carries fifty percent. The captured assignment pages show Chapter 1 and Chapter 2 submissions but do not publish their individual shares within continuous assessment, so do not infer a finer weighting from their presence.
What is published about the final exam format?
The captured university files call it a final exam and publish its fifty-percent weight. They do not state duration, sections, question count, aids or permitted materials. Historical labels in the exercise file evidence derivation, calculation and explanation question types, but they do not establish the current paper structure. Confirm operational details on Moodle.
Why can sound levels not be added directly?
Decibels are logarithmic labels for linear pressure-squared or energy quantities. Independent sources combine through those linear quantities, so each level must be converted with ten raised to level over ten, summed, and converted back once. Directly adding the labels produces a value with no physical energy interpretation.
How do I distinguish monopole, dipole and quadrupole noise?
Start with what changes in the governing balances. Fluctuating volume flow is monopole-like, unsteady force is dipole-like, and nonlinear turbulent stress is quadrupole-like. Then inspect directivity and cancellation. Real machinery often mixes them because finite size, moving surfaces and nearby boundaries prevent the compact ideal patterns from remaining pure.
What does blade-passing frequency tell me?
It identifies the primary periodic order created when each blade repeats the same event once per revolution. Multiply blade count by revolutions per second, not rpm. A matching spectral line supports a rotating periodic mechanism, but directivity, speed scaling or a geometry change is still needed to separate loading, thickness and interaction sources.
When is a plane-wave duct model unsafe?
Compare operating frequency with the first higher-mode cut-on for the duct geometry. Below cut-on, higher modes are evanescent and a plane-wave model is often a defensible start. Above it, transverse structure can propagate, so one-dimensional junction, chamber and side-branch formulas may miss modal coupling and must be qualified or replaced.
Why does a tuned resonator fail away from resonance?
At resonance, neck inertia and cavity stiffness cancel, leaving resistance to set the response. Away from resonance their reactive parts no longer cancel, neck flow falls and reflection weakens. Damping trades peak height for bandwidth, so a design must be checked at the source's frequency extremes rather than only at the target centre.
Does the captured material cover every topic in the course title?
The published outline names later topics including sound absorption, vibration isolation and design by machine learning. The detailed captured teaching files available here cover the introductory acoustics, aeroacoustic-source and duct-acoustics blocks. This guide stays within those files rather than inventing the missing later teaching content; consult Moodle as new materials appear.
Questions students ask in each MECH7029 chapter
- Why is RMS pressure used instead of average pressure?
- A sinusoidal gauge pressure spends equal time above and below the mean, so its ordinary average is zero while it still carries energy. Squaring, averaging and taking the square root preserves an energy-related magnitude in pressure units. Chapter 01 · Sound Waves, Pressure Levels and Energy
- Why is the centre of an octave not the arithmetic midpoint?
- An octave is defined by frequency ratios, so the centre must have the same ratio to each edge. The geometric mean supplies that property, while an arithmetic midpoint divides only the numerical interval and gives unequal ratios. Chapter 02 · Frequency Bands, Weighting and Level Addition
- Why can a calibrated microphone still give the wrong field result?
- Calibration verifies sensitivity under the calibrator condition. It does not correct an unsuitable directional response, reflection from the microphone body, poor position, wind or changing background. Those conditions must be controlled and documented separately. Chapter 03 · Hearing, Measurement and Noise Descriptors
- Why does temperature change in an adiabatic sound wave?
- Adiabatic means no external heat transfer, not constant temperature. Mechanical compression raises molecular energy and temperature, while expansion lowers them. The reversible changes of pressure, density and temperature are linked through the isentropic relation. Chapter 04 · Wave Equation and Acoustic State Relations
- 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. Chapter 05 · Monopole, Dipole and Quadrupole Sources
- Does the acoustic analogy require the entire flow to be linear?
- No. The propagation operator is written in wave-equation form while nonlinear flow quantities remain in equivalent source terms. Approximations enter when those terms and the surrounding propagation medium are modelled. Chapter 06 · Acoustic Analogy, Power Laws and Fan Noise
- Why are pressure and velocity nodes not at the same place?
- For a reflected plane wave, the pressure and particle-velocity reflection signs differ. Their interference patterns are therefore shifted by a quarter wavelength, so a pressure maximum coincides with a velocity minimum for ideal total reflection. Chapter 07 · Standing Waves, Junctions and Duct Modes
- Why can an expansion chamber have zero ideal loss at some frequencies?
- The reflections from its two junctions accumulate phase across the chamber. At half-wave conditions their net effect restores transmission, creating passbands despite the area mismatch. Chapter 08 · Expansion Chambers and Transmission Loss
- How is a quarter-wave branch different from a Helmholtz resonator?
- The quarter-wave branch relies on a distributed standing wave along a tube whose length is comparable with wavelength. A Helmholtz resonator is treated as compact, with lumped neck inertia and cavity compliance. Chapter 09 · Quarter-Wave and Helmholtz Resonators
How to study for the exam
Use a four-pass cycle. First, redraw the physical picture with wave arrows, source location, boundaries and the measured quantity. Second, write the controlling equation from memory together with its assumptions and units. Third, recompute one original example without looking, keeping decibel operations in linear energy and checking every rpm, RMS and effective-length conversion.
Fourth, change one fact and predict the direction before recalculating: double pressure, move above cut-on, lengthen a chamber, enlarge a cavity or shift fan speed. Finish each session with one sentence that states where the chosen model fails.
This approach prepares you for the derivation, calculation and brief physical-explanation types visible in the exercise material without pretending the historical labels define the current final exam format. In the final week, practise mixed chains that begin with a spectrum, diagnose a source and end with a control whose off-design weakness is explicit.
Confirm the current assessment logistics and later-topic coverage on Moodle.
