Virtual impedance tube

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    Experimental apparatus

    Apparatus operationAwaiting equipment checks

    Drag a part to a dashed target, or select the part and then the target. Use Tab and Enter for keyboard operation. When swapping microphones, move A to the holding rack first.

    Single-frequency sound field

    The sound field is a slowed single-frequency illustration. Acquisition uses 50–1600 Hz broadband white noise. Listening volume does not represent instrument sound pressure.

    Experiment records

    Export before refreshing. Records remain only in the current page.

    Operation log
    1. Not started.

    4 × 4 cavity TMM design

    50 × 50 mm Square panel

    Cavity parameters

    16 / 16 cells
    TypeCountCavity depth
    mm
    Hole radius
    mm
    Neck extension
    mm
    Calculation settings and baseline

    1–3 cavity types, totalling 16 cells; rows with zero count are excluded. The standard grid spans 200–2500 Hz with a 1 Hz step and 40 end-correction terms; refinement uses 0.25 Hz and 80 terms.

    Baseline: 16 identical cavities with a 0.70 mm hole radius, 20 mm cavity depth and 2 mm neck extension. This model represents the square design panel, not a reconstruction of the circular test specimen.

    Measured-data processing

    Select both records and keep A/B wiring identities unchanged.

    File format and quality assessment

    Supports the course LVM format with an empty first column(X_Columns No,Delta_X headers), or three columns containing time, channel A and channel B. Files are sent to the AANTC calculation service, processed only during the current request, and neither files nor results are saved.

    One record pair is not three independent trials. Without independent calibration, reciprocity cannot be declared acceptable. Retain α outside 0–1 to diagnose measurement and channel-mapping issues.

    B&K Type 4206100 mm Tube section50–1600 Hz
    Sample rate
    20 kHz
    FFT
    4096
    Record duration
    10 s
    Independent repeats
    3 times

    Physical laboratory procedure

    Preparation and inspection

    Check the assigned specimen ID and photograph the perforated and open-cavity faces. Inspect cracks, flatness, residual resin, blocked holes and cavity-wall damage. Record actual dimensions and environmental conditions.

    Start the signal generator, amplifier, microphone conditioner, NI acquisition system and computer. Check the empty tube and channels, save the current background and noise spectra, then calibrate according to the laboratory procedure.

    Mounting and paired acquisition

    Face the perforated side towards the source. Seal the open back with the specified uniform thin tape and press it against the rigid termination. Keep the tape type, layer count and coverage unchanged.

    Use one band-limited white-noise excitation covering 50–1600 Hz. Check both channels for overload and adequate signal-to-noise ratio. Record simultaneously for 10 s, swap the microphones without changing the excitation or mounting, and record for another 10 s.

    Assessment and independent repeats

    Correct channel amplitude and phase mismatch, then assess reciprocity and coherence. Reject reciprocity deviations above 15%. Coherence below 0.90 requires diagnosis, not automatic rejection. Retain anomalies and reasons for rejection.

    Remove the specimen, inspect the seal, rotate it by 90°, reseal and remount, then acquire the next pair. The goal is three accepted trials with independent remounting; segments of one record are not independent trials.

    Processing and reporting

    Remove the mean and segment both records using identical window, overlap and FFT settings. Average cross- and auto-spectra before taking their ratio to estimate H. Average corrected complex H over accepted trials, then recalculate R, α and Z/Z₀.

    Report trapezoidal band means, trial-level sample standard deviations and coefficients of variation for three bands. State when records are insufficient; one curve does not establish repeatability.

    Measurement principle

    Two-microphone wave decomposition

    Using ejωt convention, specimen at x=0, with microphones at x₁=−(s+l),x₂=−l.s=50 mm,l=100 mm are the nominal course values.

    p(x) = e−jkx + R ejkx
    H₁₂ = ⟨P₂ P₁*⟩ / ⟨|P₁|²⟩
    R = [(H₁₂−e−jks) / (ejks−H₁₂)] e2jk(s+l)
    α = 1−|R|²   ·   Z/Z₀ = (1+R)/(1−R)

    Training-model limitations

    The training specimen uses a passive lumped impedance z=0.85+j3.2(f/f₀−f₀/f),f₀ is approximately 960 Hz. Small resonance shifts between independent mountings support repeatability exercises; they do not represent actual BU/BG specimens.

    Each virtual record contains 200,000 samples of two-channel time histories generated by Python. Welch cross- and auto-spectra use a 4096-point periodic Hann window, 50% overlap and segment-wise mean removal. Frequency spacing is approximately 4.883 Hz; band boundaries are interpolated.

    The swapped record is reordered by physical position, and mismatch is corrected using a complex square root with continuous phase. An independently known calibration factor is also used to compare the two transfer functions H as a teaching indicator of reciprocity. This is not a validated laboratory reciprocity algorithm. Low coherence may also coincide with failed reciprocity; assess each indicator separately.

    Course requirements, historical examples and the design task

    This page uses MECH5961_Lab1_Assignment_2026.docx as the procedure baseline. The historical program in the archive absorption_impedance.m uses a 1024-point FFT and does not implement the complete three-trial, quality-control and complex-averaging workflow. It is not a complete processing program for the current assignment.

    MECH5961_TMM_design.m is a design tool for a 50 × 50 mm panel with 4 × 4 independent cavities, not a reconstruction of a circular Voronoi specimen. The TMM workspace implements this model and does not infer unknown resonance frequencies of actual circular specimens.

    The actual BU/BG specimens have hole radii of 0.75, 1.00 and 1.25 mm; BU has 42 holes and BG has 40. Cavity distributions and total open areas also differ, so differences cannot be attributed entirely to the radial gradient.

    Equipment reference:Brüel & Kjær Type 4206 Product information .Course sources: laboratory assignment, example data package and MATLAB design file.

    Calculation source
    Download tmm.pyDownload processing.py
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