Source: https://jmrplens.github.io/phonometry/materials/surfaces/road-absorption/ # In-situ Road-Surface Absorption How much sound a road surface absorbs decides how loud its traffic is, and a core cannot be cut out of a motorway and carried to a laboratory. ISO 13472 measures the absorption *in situ*, on the pavement as built, twice over. The **subtraction technique** of Part 1 fires an impulse from a loudspeaker down onto an extended surface and separates the incident and reflected components of one microphone's impulse response in time; the **spot method** of Part 2 seals a short tube onto a small patch and hands the mathematics to the impedance-tube transfer-function method. This guide covers both, from the mandatory geometry and the Adrienne window to the sampled area and the plane-wave limits of the tube, and closes with the choice between them. ## 1. Subtraction technique (ISO 13472-1) Out in the field there is no reverberation room. ISO 13472-1 measures the sound absorption of a road surface (or any extended flat surface) *in situ* by firing an impulse from a loudspeaker at height $d_\mathrm{s}$ down onto the surface and recording the impulse response at a microphone at height $d_\mathrm{m}$. The **incident** and **reflected** components are separated in time with an Adrienne window; their transfer function gives the reflection factor and hence the absorption. **Geometrical spreading (Clause 4.1).** The reflected wave travels farther than the direct wave, so it is attenuated by the geometrical-spreading factor $$ K_r = \frac{d_\mathrm{s} - d_\mathrm{m}}{d_\mathrm{s} + d_\mathrm{m}}, $$ which equals $2/3$ for the mandatory geometry $d_\mathrm{s} = 1.25$ m, $d_\mathrm{m} = 0.25$ m. The absorption follows from the windowed incident and reflected spectra $H_\mathrm{i}$, $H_\mathrm{r}$: $$ \alpha(f) = 1 - \frac{1}{K_r^2}\left|\frac{H_\mathrm{r}(f)}{H_\mathrm{i}(f)}\right|^2. $$ ```python import numpy as np from phonometry import materials # A band-limited incident impulse response and a synthetic road reflection # hr = Kr * r0 * delayed(hi): a reflection of magnitude r0 = 0.4, delayed by the # extra path, and scaled by the geometrical-spreading factor Kr. fs, n = 48000.0, 4096 t = np.arange(n) / fs hi = np.zeros(n) hi[:64] = np.hanning(64) * np.cos(2.0 * np.pi * 1500.0 * t[:64]) kr = materials.geometric_spreading_factor() # (ds - dm)/(ds + dm) = 2/3 hr = kr * 0.4 * np.roll(hi, 96) # Narrow-band absorption, then reduced to one-third octaves over 250-4000 Hz. alpha = materials.insitu_absorption_coefficient(hi, hr) # 1 - (1/Kr^2)|Hr/Hi|^2 freq = np.fft.rfftfreq(n, 1.0 / fs) centres, band = materials.one_third_octave_absorption(freq, alpha) print(round(kr, 4)) # 0.6667 print(round(float(band[2]), 3)) # 0.84 (alpha = 1 - 0.4^2 = 0.84) ``` **Adrienne window (Clause 6.4).** The time window that isolates the reflection mandates only a sharp leading edge, a 5 ms flat portion and a cosine-squared or Blackman-Harris trailing edge; the exact durations are reported per measurement, not fixed, so they are configurable here. ```python from phonometry import materials # Default: 0.5 ms leading edge, 5 ms flat top, 5 ms Blackman-Harris trailing. w = materials.adrienne_window(48000.0) print(w.shape[0]) # 504 samples at 48 kHz print(round(float(w.max()), 3)) # 1.0 (flat top and edges meet at unity) ``` **End-to-end spectrum.** `insitu_absorption_spectrum` runs the whole chain (the windowed incident and reflected impulse responses to the narrow-band absorption and on to one-third-octave bands) and returns a plottable `InsituAbsorptionResult`: ```python import numpy as np from phonometry import materials from scipy.signal import firwin, lfilter # A synthetic-but-realistic measurement. hi is a unit incident impulse; the road # reflection hr = Kr * r0 * roll(hi, shift) uses the geometrical-spreading # factor Kr, a mildly frequency-dependent r0 (a gentle low-pass, so a porous # surface reflects less as frequency rises) and the reflected-path delay # shift = round(2 dm / c * fs). fs, n = 48000.0, 8192 kr = materials.geometric_spreading_factor() # (ds - dm)/(ds + dm) = 2/3 hi = np.zeros(n) hi[0] = 1.0 taps = firwin(41, 1200.0, fs=fs) taps = taps / taps.sum() shift = int(round(2.0 * 0.25 / 340.0 * fs)) # reflected-path delay 2 dm / c hr = kr * 0.85 * np.roll(lfilter(taps, 1.0, hi), shift) result = materials.insitu_absorption_spectrum(hi, hr, fs) print(result.frequencies[[0, -1]].astype(int)) # [ 250 4000] print(np.round(result.absorption[[0, 6, 12]], 2)) # [0.31 0.65 1. ] result.plot() # alpha(f) bar chart over 250-4000 Hz (needs matplotlib) ``` *The absorption rises with frequency because the surface reflects less of the high-frequency energy, exactly as the low-pass reflection factor $r_0(f)$ dictates through $\alpha = 1 - (1/K_r^2)\,|H_\mathrm{r}/H_\mathrm{i}|^2$.*

Show the code for this figure

```python import matplotlib.pyplot as plt import numpy as np from scipy.signal import firwin, lfilter from phonometry import materials # A synthetic-but-realistic measurement. hi is a unit incident impulse; the road # reflection hr = Kr * r0 * roll(hi, shift) uses the geometrical-spreading # factor Kr, a mildly frequency-dependent r0 (a gentle low-pass, so a porous # surface reflects less as frequency rises) and the reflected-path delay # shift = round(2 dm / c * fs). fs, n = 48000.0, 8192 kr = materials.geometric_spreading_factor() # (ds - dm)/(ds + dm) = 2/3 hi = np.zeros(n) hi[0] = 1.0 taps = firwin(41, 1200.0, fs=fs) taps = taps / taps.sum() shift = int(round(2.0 * 0.25 / 340.0 * fs)) # reflected-path delay 2 dm / c hr = kr * 0.85 * np.roll(lfilter(taps, 1.0, hi), shift) result = materials.insitu_absorption_spectrum(hi, hr, fs) # result is the InsituAbsorptionResult computed above. One line: result.plot() plt.show() # By hand: a bar chart of alpha over the one-third-octave bands. freqs = result.frequencies positions = np.arange(freqs.size) fig, ax = plt.subplots() ax.bar(positions, np.nan_to_num(result.absorption), width=0.7, color="#1f77b4") ax.set_xticks(positions) ax.set_xticklabels([f"{f:g}" for f in freqs], rotation=45, ha="right") ax.set_xlabel("Frequency [Hz]") ax.set_ylabel("Absorption coefficient alpha") ax.set_ylim(0.0, 1.0) ax.set_title("In-situ road-surface absorption (ISO 13472-1)") plt.show() ```

**Maximum sampled area (Annex A).** The finite time window limits how much of the surface contributes to the reflection. The maximum sampled area is a circle whose radius the library computes from the geometry and window width; the Annex A worked example ($d_\mathrm{s} = 1.25$ m, $d_\mathrm{m} = 0.25$ m, $c = 340$ m/s, 5 ms flat window) gives about 1.34 m. ```python from phonometry import materials print(round(materials.max_sampled_area_radius(5.0e-3), 3)) # 1.343 (metres) ``` The whole arrangement fits in one to-scale drawing. `plot_insitu_geometry` draws the standard set-up with that sampled radius on the surface, and a measured `InsituAbsorptionResult` that retained its heights redraws its own with `result.plot_geometry()`. *The standard geometry to scale: source at 1.25 m, microphone at 0.25 m on the same vertical, and the 5 ms window turned into the 1.34 m radius of road that actually contributes to the reflection.*

Show the code for this figure

```python import matplotlib.pyplot as plt from phonometry import materials # The standard geometry: source at 1.25 m, microphone at 0.25 m, and the # 1.34 m sampled-area radius of the 5 ms window. materials.plot_insitu_geometry() plt.show() # A measured spectrum retains its heights and redraws its own set-up: # result = materials.insitu_absorption_spectrum(hi, hr, fs) # result.plot_geometry() ```

## 2. Spot method (ISO 13472-2) For smaller patches, ISO 13472-2 seals a short circular tube onto the surface and measures the absorption with the two-microphone transfer-function method of ISO 10534-2. The library provides the spot-method geometry and validity helpers; the transfer-function DSP itself is the impedance-tube routine `two_microphone_impedance` (see [Impedance Tube](https://jmrplens.github.io/phonometry/materials/absorbers/impedance-tube/)). The apparatus is a portable impedance tube stood on end: a loudspeaker at the top, two flush-mounted microphones at spacing $s$ in the tube wall, and the road surface itself as the sample. A test fixture with a ring of deformable material (a rubber O-ring or similar) makes an airtight seal between the tube mouth and the pavement, so the patch under the mouth, not the leak around it, terminates the tube; the underside of that sealing device defines the plane of reference at which the reflection factor is evaluated. The method is written for **reflective** surfaces, dense asphalts and test tracks per ISO 10844 rather than open porous layers: the standard declares it unreliable once the measured absorption coefficient exceeds 0.15, and no longer calls a surface reflective above 0.10, because on an absorbing surface the reflected wave the two microphones must resolve all but vanishes. The tube samples only the circle under its mouth, so one reading is a spot in the statistical sense too: on regular roads the standard spaces measurement positions over the area of interest with an emphasis on the wheel tracks (as a guideline, one position every 10 m), on a surface that must be smooth, flat, free of debris and dry. **Plane-wave limits (Clause 5.4).** The tube supports only plane waves below $$ f_\mathrm{u} = 0.58\,\frac{c_0}{d}, $$ with $d$ the tube diameter, and the microphone spacing $s$ must sit between $0.05\,c_0/f_\mathrm{min}$ and $0.45\,c_0/f_\mathrm{max}$. The reported range is the one-third-octave bands 250–1600 Hz. ```python from phonometry import materials # Upper usable frequency of a 100 mm tube and the valid spacing window. print(round(materials.spot_tube_upper_frequency(0.100, 343.0), 1)) # 1989.4 Hz s_min, s_max = materials.spot_microphone_spacing_bounds( 343.0, f_min=220.0, f_max=1800.0) print(round(s_min, 3), round(s_max, 3)) # 0.078 0.086 (metres) ``` The frequency window is the price of portability: the tube diameter that keeps the mouth sealable on real pavement caps the upper bands at 1600 Hz, and the tube length caps the lower ones at 250 Hz, a narrower window than the 250–4000 Hz of the subtraction technique. Within it, the reduction is the ISO 10534-2 chain unchanged: the transfer function between the two microphones separates incident and reflected waves, and the standard's Annex A additionally subtracts the internal losses of the system (measured once against a rigid plate) so the tube's own dissipation is not billed to the road; that correction is `spot_internal_loss_correction`. Nothing in code enforces the acquisition around either method: the averaging, the free-field reference, the signal-to-noise checks, the seal verification and the weather limits are the operator's, and the library only sees the two impulse responses (or the transfer function) that come out of them. ## Subtraction or spot? The two parts of ISO 13472 are complements, not competitors, and Part 2's own introduction says both should give similar results between 315 Hz and 1600 Hz while their fields of application differ: - **Surface type.** The subtraction technique handles the full range from reflective to highly absorbing (porous asphalt included); the spot method is scoped to reflective surfaces and declared unreliable above a measured absorption of 0.15, where its confined reflected wave is no longer strong enough to resolve. - **Sampled area.** The subtraction technique averages over a patch whose Annex A clear zone extends to the 1.34 m maximum sampled-area radius of section 1 (about 5.6 m² of pavement, with the area actually contributing at each frequency set by the time window), a fair sample of texture and joints; the spot method sees only the patch under the tube mouth, so it trades spatial representativeness for the ability to sit on a narrow strip, a wheel track, or a laboratory core. - **Bandwidth.** 250–4000 Hz against 250–1600 Hz, which matters because the tyre-road noise the measurement usually serves peaks around 1 kHz but has content beyond the spot method's ceiling. - **Logistics.** The subtraction rig needs a mast, a free-field reference measurement and a pause in traffic; the spot tube needs a flat, sealable patch and minutes per point. Surface types and acceptance criteria aside, that practical difference is usually what decides. Both methods report the same quantity, the normal-incidence absorption coefficient in one-third-octave bands, so a low-absorption lane can be surveyed with the spot tube and anchored with a subtraction measurement at a few positions. ## See also - [Impedance Tube](https://jmrplens.github.io/phonometry/materials/absorbers/impedance-tube/): the ISO 10534-2 two-microphone method the spot tube defers its mathematics to, and the laboratory instrument the spot method miniaturises. - [Diffusers and Their Coefficients](https://jmrplens.github.io/phonometry/materials/diffusers/diffusers/): the other family of surface measurements, grading where a surface sends its reflection rather than how much it absorbs. - [Sound Absorption Measurement and Rating](https://jmrplens.github.io/phonometry/materials/absorbers/absorption-measurement/): the laboratory (reverberation-room) absorption measurement and its rating, for materials that can be brought indoors. - [Outdoor Sound Propagation](https://jmrplens.github.io/phonometry/environment/propagation/outdoor-propagation/): where the absorption of the ground surface enters the propagation models. - API reference: [`materials.surfaces.road_absorption`](https://jmrplens.github.io/phonometry/reference/api/materials/road-absorption/). ## References - International Organization for Standardization. (2002). *Acoustics — Measurement of sound absorption properties of road surfaces in situ — Part 1: Extended surface method* (ISO 13472-1:2002, the edition implemented here; since revised as [ISO 13472-1:2022](https://www.iso.org/standard/77032.html)). [iso.org catalogue](https://www.iso.org/standard/35387.html). The subtraction technique of section 1: the mandatory geometry, the Adrienne window and the Annex A sampled-area radius. - International Organization for Standardization. (2010). *Acoustics — Measurement of sound absorption properties of road surfaces in situ — Part 2: Spot method for reflective surfaces* (ISO 13472-2:2010, the edition implemented here; since revised as [ISO 13472-2:2025](https://www.iso.org/standard/84925.html)). [iso.org catalogue](https://www.iso.org/standard/32304.html). The spot method of section 2: the plane-wave limits, the microphone spacing window and the deferral to ISO 10534-2. - International Organization for Standardization. (1998). *Acoustics — Determination of sound absorption coefficient and impedance in impedance tubes — Part 2: Transfer-function method* (ISO 10534-2:1998). [iso.org catalogue](https://www.iso.org/standard/22851.html). The two-microphone transfer-function reduction the spot method reuses, implemented in the [Impedance Tube](https://jmrplens.github.io/phonometry/materials/absorbers/impedance-tube/) guide. ## Standards ISO 13472-1:2002 (in-situ absorption, extended surface) and ISO 13472-2:2010 (in-situ absorption, spot method); the spot method's transfer-function DSP is the ISO 10534-2:1998 routine of the [Impedance Tube](https://jmrplens.github.io/phonometry/materials/absorbers/impedance-tube/) guide. Both road standards have since been revised (ISO 13472-1:2022, ISO 13472-2:2025); the earlier editions are the implemented ones. Numerical conformance against the standards' worked examples and closed forms is tracked in [CONFORMANCE.md](https://jmrplens.github.io/phonometry/reference/conformance/).