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Parameter · 07 Run Settings

Frequency spacing

acoustics.frequency.spacing Step 07 · Run Settings

Selects how the frequencies of the acoustic sweep are chosen: linear (every Δf\Delta f), logarithmic (a number of frequencies evenly spaced in log⁡f\log f), octave or 1/3 octave (a range of bands, each solved at its lower edge, centre and upper edge), or custom (a typed list).

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Theory

  • Linear: fmin,fmin+Δf,…f_{min}, f_{min}+\Delta f, \ldots up to fmaxf_{max} (Frequency step).
  • Logarithmic: nn frequencies with a constant ratio between neighbours (Number of frequencies (logarithmic)).
  • Octave / 1/3 octave: the bands between a first and a last nominal centre frequency (Band range). Each band is solved at three frequencies: its lower edge fLf_L, its nominal centre fCf_C and its upper edge fUf_U, with base-2 edges, equation (1). An edge shared by two neighbouring bands (exact octave multiples such as 125 / 250 / 500 Hz) is solved once. fminf_{min} and fmaxf_{max} become fLf_L of the first band and fUf_U of the last.
  • Custom: the typed frequencies, separated by commas; they are sorted, repeats are removed, and at least two are required.

For an octave or 1/3-octave sweep, the band transmission loss (and band insertion loss) is the energy mean of exactly the band's own three points by Simpson's rule in ln⁡f\ln f, equation (2). Because fLf_L, fCf_C and fUf_U are equally spaced in ln⁡f\ln f, the weights are 1/6, 4/6, 1/6. A band whose three points are not all present falls back to the plain mean. With linear, logarithmic or custom spacing, the band table uses exact base-2 1/3-octave bands and the plain energy mean of all frequencies inside each band, equation (3).

Equations

fL=fC 2−b,fU=fC 2b,b=12 (octave), 16 (1/3 octave)f_L = f_C\,2^{-b}, \qquad f_U = f_C\,2^{b}, \qquad b = \tfrac{1}{2}\ \text{(octave)},\ \tfrac{1}{6}\ \text{(1/3 octave)}
(1)
TLband=−10log⁡10(16 10−TL(fL)/10+46 10−TL(fC)/10+16 10−TL(fU)/10)TL_{band} = -10\log_{10}\left(\tfrac{1}{6}\,10^{-TL(f_L)/10} + \tfrac{4}{6}\,10^{-TL(f_C)/10} + \tfrac{1}{6}\,10^{-TL(f_U)/10}\right)
(2)
TLband=−10log⁡10(1N∑fj∈[fL,fU)10−TL(fj)/10)TL_{band} = -10\log_{10}\left(\frac{1}{N}\sum_{f_j \in [f_L, f_U)} 10^{-TL(f_j)/10}\right)
(3)
wheremeaningunit
fCf_CNominal centre frequency of the bandHz
fL,fUf_L, f_ULower and upper band edgesHz
bbHalf band width in octaves-
TLTLTransmission loss at a solved frequencydB
NNNumber of solved frequencies inside the band-

Default and rule

Default
linear
Rule

Linear.

Source

The band edges and the Simpson band average are the program's own construction, validated on a 1/3-octave sweep of the expansion chamber, 100-1000 Hz (10 bands, 30 solves). The nominal centre frequencies are the ISO 266 preferred values.

Valid range linear | log | octave | third_octave | custom

Choice

Linear, logarithmic, octave, 1/3 octave, custom. With octave, 1/3-octave and custom spacing, fminf_{min} and fmaxf_{max} are locked to the solved range.

Nominal centres

The edges are computed from the NOMINAL centres (63, 125, ...), not from exact base-2 centres, so the edge of a neighbouring band can fall just inside a band (125/2\sqrt{2} = 88.4 Hz < 63 2\sqrt{2} = 89.1 Hz); such a point is not counted in that band.