Calculate radiated SPL

Computes the sound pressure level that the muffler radiates to a microphone near its outlet, at each calculation frequency, from an entered source spectrum and the computed insertion loss. The calculation requires the insertion loss, so enabling this option also enables the insertion loss.

Last updated 2026-11-11

Theory

The source is entered per calculation frequency as either a sound power level or a sound pressure level (Source quantity). It can be typed, pasted, or imported from a text or spreadsheet file; imported values are interpolated linearly in $\log f$ and never extrapolated. The muffler reduces the source by the insertion loss of the whole muffler (all outlets together). For a sound power source, the level at the microphone then follows a point-source propagation model in the form of ISO 9613-2, equation (1):

directivity $D_c = 10\lg Q$ with $Q = 2$ : one perfectly reflecting ground plane, i.e. hemispherical radiation;
geometrical divergence $A_{div} = 20\lg(d/1\,\mathrm{m}) + 11$ dB, i.e. $10\lg(4\pi d^2)$ ;
air absorption $A_{atm} = \alpha d$ with the attenuation coefficient of ISO 9613-1 (Ambient air temperature, with the relative humidity and the ambient pressure of the Material step's Ambient air).

No other term of ISO 9613-2 is applied (ground effect beyond $Q$ , barriers, meteorological correction). For a source SPL measured with the reference pipe at a distance $d_s$ , the program transfers the level from $d_s$ to $d$ , equation (2); $Q$ cancels, and $d_s = d$ gives the source SPL minus the insertion loss.

The results are also A-weighted, equation (3) (IEC 61672-1, 2013), and summed to overall levels, equation (4); the overall level is meaningful only when the entries are the line or band levels of a single spectrum. Results are written to acoustics/spl.csv, to the sheet "Radiated SPL" of the results workbook and to the report. After a change of the source table, the levels are recomputed from il.csv when the report is regenerated, without a new solve.

Equations

L_p = L_W - IL + 10\lg Q - \left(20\lg\frac{d}{1\,\mathrm{m}} + 11\right) - \alpha d

(1)

L_p = L_{p,src} - IL - 20\lg\frac{d}{d_s} - \alpha\,(d - d_s)

(2)

L_{pA} = L_p + A(f), \qquad A(f) = 20\lg R_A(f) + 2.00, \qquad R_A = \frac{12194^2 f^4}{(f^2 + 20.6^2)\sqrt{(f^2 + 107.7^2)(f^2 + 737.9^2)}\,(f^2 + 12194^2)}

(3)

L_{tot} = 10\lg\sum_j 10^{L_j/10}

(4)

where	meaning	unit
$L_W$	Source sound power level, re 1 pW	dB
$L_{p,src}$	Source sound pressure level at $d_s$ (reference pipe), re 20 µPa	dB
$IL$	Insertion loss of the muffler	dB
$Q$	Directivity factor, 2	-
$d$	Distance outlet orifice to microphone	m
$d_s$	Distance at which the source SPL was measured	m
$\alpha$	Atmospheric attenuation coefficient	dB/m
$L_p, L_{pA}$	Radiated sound pressure level, unweighted and A-weighted	dB, dB(A)
$f$	Frequency (in $R_A$ : in Hz)	Hz

Default and rule

Default: offMeasured
Rule: Off. A run with the option on and no source level entered is refused at start.
Source: The directivity factor $Q = 2$ , the ISO 5130 measurement position and the distance correction for an SPL source are program choices. The attenuation coefficient reproduces 1789 of 1848 tabulated ISO 9613-1 values within 0.5 % (median 0.07 %); the other 59 differ because of transcription errors in the tabulation. The calculation was validated by a run of the expansion chamber with insertion loss and radiated SPL. The method follows ISO 9613-1, ISO 9613-2 and ISO 5130, cited by their standard numbers.

Valid range on | off; switches the insertion loss on

Point source

Below $f = c/(2\pi d)$ the microphone is within a sixth of a wavelength of the outlet ( $kd < 1$ ); the spreading law is then only an approximation, and the report states this.

Insertion-loss validity

Where the insertion loss is flagged (a non-plane mode at an outlet), the radiated SPL inherits the flag.

Not with mean-flow convection

The radiated SPL is computed from the insertion loss, so it is switched off together with it while Mean-flow convection is on: the radiated power at an outlet with mean flow cannot yet be computed reliably (see Compute the insertion loss).

References 1

International Electrotechnical Commission (2013). Electroacoustics - Sound level meters - Part 1: Specifications. IEC 61672-1:2013. Web page

Theory

Equations

Default and rule

Valid range on | off; switches the insertion loss on

Related 8

References 1