© ISO 2016 Acoustics — Objective method for assessing the audibility of tones in noise — Engineering method Acoustique — Méthode objective pour évaluer l’audibilité des tons dans le bruit — Méthode d’[.]
General
The measurement procedure is determined by specific objectives, necessitating careful consideration of factors such as the selection of measurement points, timing, duration, and the presence of extraneous noise to ensure accurate assessment.
The audibility of prominent tones is determined by the sound pressure, denoted as p(t) For frequency analysis, the A-weighted equivalent continuous sound pressure level, L Aeq, must be established for the relevant spectral lines, as specified in ISO 1996-1 If the spectrum is unweighted (linear), it should be adjusted to A-weighting following the guidelines of IEC 61672-1.
Measurement instruments
Sound level meters must comply with Class 1 standards outlined in IEC 61672-1 These meters should feature frequency weighting options of “A”/“LIN” or “A”/“Z,” with a lower limit frequency of 20 Hz or lower.
Recording instruments, including digital and magnetic tape, can be utilized to obtain measured values These values must adhere to the tolerance range specified in IEC 61672-1.
The analysis of frequency components in measurement signals is conducted with a frequency analyzer, ensuring a constant line spacing, Δf, between 1.9 Hz and 4 Hz The use of the Hanning window is required in this Publicly Available Specification Additionally, it is essential that the digitalization of the sound pressure signal maintains a resolution of at least 0.1 dB across the entire utilized dynamic range.
To ensure accurate frequency analysis, the analogue measurement signal must first be filtered through a steep low-pass filter, known as an antialiasing filter The sampling frequency should be at least double the maximum usable frequency Additionally, a Hanning window should be applied as the time window to minimize lateral bands.
Merging the basic spectra
The prominent tone assessment will utilize spectra with an averaging time of about 3 seconds Given the line spacing of 1.9 Hz to 4 Hz and a typical frequency range of a few kHz, the basic spectra from the frequency analyzer will have an averaging time of less than 1 second To achieve the desired averaging time of approximately 3 seconds, multiple basic spectra will be combined line by line using Formula (1).
L i,j is the level of the ith spectral line for the jth spectrum;
N is the number of merged spectra.
General information
The evaluation aims to determine audibility, denoted as ΔL, using a consistent procedure for both stationary and non-stationary noises For barely perceptible tones, a quaver (eighth note) serves as an adequate base time for hearing However, extensive research indicates that the procedure's lower limit is approximately 3 seconds for averaging times Shorter averaging times can yield inaccurate audibility values, either too high or too low Additionally, signals with significant dynamic levels that exceed the 3-second averaging cannot be assessed using this Publicly Available Specification Specific conditions must be met for accurate measurements.
The extended uncertainty, U, for audibility, ΔL, must not exceed ±1.5 dB with a 90% coverage probability in a bilateral confidence interval This requirement is typically met when evaluating at least 12 time-staggered narrow-band averaged spectra If fewer than 12 averaged spectra are available, the uncertainty should be assessed as specified in Clause 6.
— Where there are alternating operating states, all of the operating states shall be covered by the averaging spectra used (see Annex E).
Tonal components within distinct critical bands are assessed individually, focusing solely on the most prominent tone to determine tonal audibility When multiple tones exist in a critical band, their tone levels, denoted as LTi, are summed to produce an overall tone level, L T (refer to section 5.3.8).
A tonal audibility occurs for a tone when its distinctness is at least 70% This requirement leads to a maximum bandwidth, \$\Delta f_R\$, that is dependent on the tone frequency, and necessitates an edge steepness of at least 24 dB/octave.
NOTE 1 For the distinctness of a tone, see 5.3.4.
NOTE 2 Harmonic multiples of a tone are evaluated, independently of that tone, similarly to all other components of the spectrum.
A sample program to determine audibility can be downloaded from http://standards.iso.org/iso/20065
Width Δf c of the critical band
The width Δfc of the critical band about the tone frequency fT is given by Formula (2):
Assuming a geometric position of the corner frequencies of the critical band (see Annex B), these corner frequencies, f1 and f2, are derived as follows: f T = f 1 × f 2 (3) f f f f
Determination of prominent tones
General information
The audibility of a tone is influenced by its tone level, \( L_T \), and the critical band level, \( L_G \), of the masking noise surrounding the tone frequency, \( f_T \) The tone frequency is identified by analyzing the frequency of all maxima in the spectrum.
The Hanning window is recommended for use, as detailed in Annex A Unlike rectangular windows, window functions increase the effective analysis bandwidth, \$\Delta f_e\$, beyond the ideal filter bandwidth, \$\Delta f\$, leading to overlapping individual bands Consequently, during the summation process, energy components are counted multiple times, with further details available in Annex A.
In a frequency analyzer, the impact of summation (when the number of lines is greater than one) is accounted for using a correction value If the analyzer program simulates level addition, this correction value must be integrated into the computing program, affecting both the tone level formation and the calculation of masking noise.
Determination of the mean narrow-band level L S of the masking noise
The mean narrow-band level, LS, is calculated through an iterative process that begins by averaging the energy of all lines within the critical band, excluding the line being analyzed In subsequent iterations, any lines exceeding the previously determined energy mean by more than 6 dB are excluded from the averaging The process continues until the new energy mean value is within ±0.005 dB of the previous value or if fewer than five lines contribute to the mean on either side of the line under investigation Ultimately, the mean narrow-band level is derived from the last iteration where at least five energy-averaged levels were present on both sides of the line.
To determine the mean narrow-band level, the entire critical band around the line under investigation is utilized, ensuring that the frequency range does not exceed the usable frequency \( f_N \) This limitation applies to both the upper limit of the highest critical band and the lower limit of the lowest critical band considered As this Publicly Available Specification is applicable only to tone frequencies of 50 Hz or higher, and since typical analyzers produce line spectra starting from 0 Hz, no special precautions are typically required.
The mean narrow-band level LS is given by Formula (6):
Li is the narrow-band level of the ith spectral line, in decibels (dB);
In the critical band, the number of spectral lines to be averaged is denoted as M The line spacing is represented by Δf, measured in Hertz (Hz) The effective bandwidth, Δf e, is also expressed in Hz; when utilizing a Hanning window, the effective bandwidth is 1.5 times the frequency resolution, Δf.
If the spectrum is unweighted (linear), then it shall be A-weighted in accordance within IEC 61672-1.
NOTE 1 If the iteration is discontinued, because the remaining number of spectral lines to be averaged on one or both sides falls below 5, then the audibility may be somewhat greater than the audibility calculated with this mean narrow-band level.
NOTE 2 The iteration procedure is described in Annex D.
NOTE 3 Using a digital calculation program, the equal condition in the iteration procedure is typically given by the resolution of the number format (high resolution should be used).
Determination of the tone level L T of a tone in a critical band
The tone level \( L_T \) is established based on the spectral line levels within the critical band around frequency \( f_T \) that contribute energy to the tone A tone can only be identified if the level of the relevant spectral line exceeds the mean narrow-band level \( L_S \) by at least 6 dB.
When analyzing tone energy, it is essential to consider multiple spectral lines due to factors such as the Picket fence effect and minor frequency fluctuations during data capture.
Neighbouring spectral lines should be used for summation purposes if
— they differ from the narrow-band level at a frequency, fT, by less than 10 dB, and
— they differ from the mean narrow-band level, LS, of the masking noise within the critical band about the tone by more than 6 dB.
Li is the narrow-band level of the ith spectral line of this critical band with tone energy, in decibels (dB);
K is the number of spectral lines with tone energy; Δf is the line spacing, in Hertz (Hz) (see 3.13); Δfe is the effective bandwidth, in Hertz (Hz) (see 5.3.2).
NOTE The individual levels of the spectral lines with tone energy [see Formula (8)] also contain energy components of the masking noise These can generally be neglected.
Distinctness of a tone
The clarity of a tone is influenced by its bandwidth and the sharpness of its edges; if these criteria are not met, the tone may be inaudible to people with normal hearing.
A tone characterized by bandpass noise exhibits a distinctness of 70% when compared to a sinusoidal tone Consequently, the maximum allowable bandwidth, denoted as ΔfR, can be approximated as a function of the tone frequency, fT, as illustrated in Figure 1 of Reference [8].
The bandwidth of a tone with a frequency f T is derived from the number of spectral lines K [see Formula (8)], multiplied by the line spacing, Δf.
First criterion: The bandwidth of the tone shall not exceed the maximum permitted bandwidth given by Formula (9).
Second criterion: The edge steepness shall be at least 24 dB/octave.
The level differences between the maximum narrow-band level of the tone, denoted as \$LT_{max}\$, and the narrow-band levels of the first spectral line below the tone, \$L_u\$, and above the tone, \$L_o\$, are calculated as follows:
The lower level difference ΔLu is given by Formula (10):
The equation \$2 \cdot 24 \, \text{dB} (10)\$ defines the relationship between the frequency of the first spectral line below the tone, denoted as \$f_u\$ in Hertz (Hz), and the frequency of the maximum narrow-band level, represented as \$f_T\$ in Hertz (Hz).
The upper level difference ΔLo is given by Formula (11):
24 (11) where fo is the frequency of the first spectral line above the tone, in Hertz (Hz); f T is the frequency of the maximum narrow-band level, in Hertz (Hz).
Determination of the critical band level, L G , of the masking noise
The level LG is given by Formula (12):
L S represents the mean narrow-band level, as detailed in section 5.3.2 The term Δfc refers to the width of the critical band surrounding the tone frequency, fT, measured in Hertz (Hz), as explained in section 5.2 Additionally, Δf denotes the line spacing or frequency resolution, also expressed in Hertz (Hz).
Masking index
The masking index, av, is given by Formula (13): a f v Hz
(13) where f is the frequency, in Hertz (Hz).
NOTE For information on the masking index, av, see Annex C.
Determination of the audibility, ΔL
The audibility ΔL between the tone level LT (see 5.3.3) and the level of the masking threshold (see 3.15) is given by Formula (14):
LT is the tone level, in decibels (dB) (see 5.3.3);
L G is the masking noise, in decibels (dB) (see 5.3.5); av is the masking index, in decibels (dB) (see 5.3.6).
NOTE Formula (14) holds correspondingly if all the parameters of that formula are given.
Determination of the decisive audibility, ΔL j , of a narrow-band spectrum
To assess the audibility ΔL of noise, multiple narrow-band spectra with identical line widths and quantities are utilized, staggered in time Each spectrum's measurement duration should be around 3 seconds The key audibility ΔLj for each spectrum is established through a systematic four-step process, omitting the run index j for clarity.
Each spectral line, i, is investigated in ascending sequence to establish whether it represents a potential tone A narrow-band level is a potential tone if the following conditions are satisfied:
Li > Li+1 and Li > Li−1 (15) and
NOTE 1 Mean narrow-band level, LSi, see 5.3.2.
The tone levels, denoted as LTk, are established for all potential tones by indexing k Additionally, the masking noises, represented as LGk, and the masking index, avk, are identified for the tone levels that meet the distinctness condition These parameters are essential for calculating the corresponding audibilities, ΔLk, as outlined in Formula (14).
If ΔL k > 0, then a tone is present.
Critical bands with the width Δf c m are formed about each of these audible tones, L Tm (run index m across all audible tones) of frequency fTm.
When multiple tones exist within a critical band, the energy levels of these tones, denoted as \( LT_{m,n} \) (where \( n \) represents the index of each tone in the band and \( H \) is the total number of tones), are combined to calculate their total energy.
H is the total number of all tones in the critical band;
LTm,n is the tone level with the run index m across all audible tones and the run index n across all tones in the critical band, in decibels (dB).
The energy of individual spectral lines can simultaneously correspond to multiple neighboring tones However, when combining the tone levels of these neighboring tones, the energy of each spectral line should not be counted more than once.
The tone frequency, f Tm , is the frequency of the most pronounced tone, i.e the tone with the greatest audibility, ΔLm,n.
The mean narrow-band level of the masking noise is derived from the iterative procedure outlined in section 5.3.2, specifically referenced in Formula (6), which relates to the tone frequency in question.
The level of the masking noise is the critical band level, LGm,n, calculated with this mean narrow-band level in accordance with 5.3.5.
This tone level, LTm, is used to recalculate the decisive audibility, ΔLk (see Step 2).
When two tones with frequencies, fT1 and fT2, are present within a single critical band, they are assessed individually if both frequencies are below 1,000 Hz The frequency difference is calculated using the formula \$f_D = f_{T1} - f_{T2}\$, where \$f_{T1}\$ and \$f_{T2}\$ are both less than 1,000 Hz.
Formula (18) exceeds the following value (see Annex B): f f
50 Hz < fT < 1 000 Hz; f T is the frequency of the more pronounced tone (the tone with the greater audibility, ΔL k ).
NOTE 2 If precisely 2 tones are present in a critical band below 1 000 Hz, then the human ear can distinguish differences less than half the critical bandwidth (see Reference [6] and Annex B).
The audibility with the maximum value, ΔL k , is the decisive audibility, ΔL j , of the individual spectrum.
Determination of the mean audibility ΔL of a number of spectra
The decisive audibility, denoted as ΔLj, is computed for each narrow-band averaged spectrum, where j represents the run index and J indicates the total number of runs The average of these J audibilities, ΔLj, is then calculated in energy terms to produce a final value of ΔL.
10?lg 1 1 10 0 1 , / dB dB (20) where ΔL j is the decisive audibility, in decibels (dB); j is the run index;
J is the number of spectra.
Tone frequencies refer to the specific frequencies assigned to audibilities To maintain an adequate separation from positive audibilities, denoted as ΔL j, a standard value of ΔL j = −10 dB is applied for all spectra that do not contain a tone.
No tone frequencies are stated for this ΔL j
The audibilities, denoted as ΔLj, are averaged in energy terms rather than using tone levels, LTj, due to the varying tone frequencies in individual spectra, which result in different masking indices, av, as outlined in Formula (13).
6 Calculation of the uncertainty of the audibility ΔL
The mean audibility, denoted as ΔL, is determined by calculating the difference between the tone level and the masking threshold level of a noise This calculation utilizes Formula (20) based on the decisive audibilities, ΔL j, derived from individual narrow-band spectra, as referenced in sections 5.3.8 and 5.3.9.
10 0 1 lg 1 , / dB dB ΔL j is calculated through the use of Formula (14) and Formula (12):
, , 10lg , with the expressions of
NOTE All frequencies are expressed in Hertz.
A normal distribution within the level zone is to be assumed for the term 10 lg ∆
No uncertainty is assumed for the masking index, av.
The LT,j values are calculated through summation, while the LS,j values are obtained by averaging intensities, necessitating the assumption of a normal distribution within the intensity range To streamline the process, a normal distribution is assumed for all summands within the sound level range Understanding the probability of underestimating tonal audibility is crucial for assessing uncertainty Notably, the upper limit of the confidence interval reveals that uncertainties in the level zone are greater than those in the intensity zone, making this agreement a reliable estimation.
Multiple incoherent sound sources influence the emission point, producing output levels that are statistically uncorrelated This leads to considerations of uncertainty in the context of LT.
LS relies solely on the uncertainty associated with the spectral lines involved, while the contribution of specific spectral lines to LT/LS is overlooked in this analysis of uncertainty.
These assumptions are used to determine the uncertainty of the audibility, ΔLj, using the Gaussian uncertainty propagation principle: σ δ δ σ δ δ σ
The three expressions above are determined in Formula (23) to Formula (25):
(23) where K is the number of all tone-containing narrow-band levels that result in the tone level, L T , in accordance with 5.3.3 and 5.3.8.
In accordance with section 5.3.8 Step 3, when summing a specified number (N) of tone levels, the total of all narrow-band levels containing tones within the impacted critical band should be utilized for the calculation of K.
M is the number of narrow-band levels that contribute to the formation of the mean narrow-band level in the critical band in question.
The uncertainty of the critical bandwidth Δf c maximally corresponds to the line spacing Δf No uncertainty is assumed for this line spacing It follows from this that σ ∆ f = ∆f c j δ δ ∆ σ
A uniform value of σ L j , =3 dB is assumed for the uncertainty of all narrow-band levels Formula (23) to Formula (25) can be used to calculate the uncertainty, σ ∆ L j , of the audibility ΔLj: σ ∆ =
The uncertainty of the mean audibility, ΔL, is given by Formula (28): δ δ ∆ σ σ
I is the number of narrow-band spectra.
The coverage factor, k, for a 90 % coverage probability in a bilateral confidence interval has a value of 1,645.
The experience also shows that with fluctuating noise, one achieves an extended uncertainty, U, of the audibility, ΔL, of about ±1,5 dB with 12 averages.
To achieve the desired level of uncertainty, a minimum of 12 spectra with an averaging time of approximately 3 seconds is required, even in the presence of significant noise fluctuations, such as those from wind turbines The exact number of spectra needed may vary based on the variability of the noise.
7 Recommendations on the presentation of results
Measurement
a) Date and place of measurement.
Acoustic environment
The measurement environment is characterized by the specific location of the source and the measurement point, accompanied by a sketch that illustrates the surrounding area and provides a physical description of the environment Key atmospheric conditions include air temperature measured in degrees Celsius, air pressure in Pascals, and relative humidity levels Additionally, the mean wind speed and direction are recorded to assess their impact on the measurements Notably, any significant information regarding dominant and fluctuating sources in the vicinity is also documented to enhance the understanding of the measurement context.
Instruments for measurement, recording and evaluation
a) The manufacturer. b) Designation/model. c) Serial number.
Acoustic data
The article discusses key aspects of line spacing and the range investigated, emphasizing the importance of noise spectra with a calculated decisive audibility, where tone frequencies and their corresponding audibilities are analyzed Additionally, it highlights the significance of the averaged noise spectrum.
1) the mean audibility, ΔL (see 5.3.9), and
If fewer than 12 spectra are averaged, the extended uncertainty must be considered Additionally, a diagram should illustrate the narrow-band levels across the frequency of the 3-second averaged spectrum that exhibits the largest ΔL.
Annex A (informative) Window effect and Picket fence effect
In the Fast Fourier Transform (FFT), the noise is determined in data blocks of block length N of the time window N corresponds to the number of sampling values, e.g 2 10 = 1 024 [5 ]
For accurate FFT analysis, the time data set must be periodic, as defined by the Fourier integral Using a rectangular time window for data processing yields correct results only for transient signals or those that fit perfectly within the window, completing whole periods However, applying this method to stochastic noises can cause significant spectral distortions due to signal truncation at the window edges.
The "smearing" of frequency lines, known as the leakage effect, occurs when a signal is multiplied by a weighting function that reduces amplitude values to zero at the edges of the time window This approach effectively addresses discontinuities in the signal within the window The specific weighting functions, denoted as w(t), are outlined as follows:
— for the rectangular window: w(t) = 1 for 0 ≤ t < T and w(t) = 0 for all other values of t;
— for the Hanning window: w(t) = 1 − cos(2πt/T) for 0 ≤ t < T and w(t) = 0 for all other values of t. NOTE T corresponds to the width of the time window.
The Hanning window is essential in this annex, as it affects the superimposition of individual filter bands based on the chosen weighting function The effective bandwidth, Δfe, with the Hanning window is 1.5 times the frequency resolution, Δf, resulting in each frequency band containing energy components from neighboring bands Consequently, power components are counted multiple times during the summation process To accurately determine the level with the Hanning window, it is necessary to include at least three lines, and these influences are accounted for through a correction value in the frequency analyzer, ensuring that the number of lines exceeds one.
The calculation of 10 lg (1/1.5) dB results in a value of -1.76 dB When simulating level addition in a program, it is essential to incorporate this correction value in the computations, affecting both the derivation of the tone level and the calculation of masking noise.
The "picket fence effect" occurs when noise is analyzed using discrete filters, resembling a view through a lattice fence This analysis leads to varying amplitude and frequency errors, influenced by the alignment of the FFT spectrum's analysis frequency with the individual tone's frequency Using a Hanning window, the amplitude error, denoted as ΔL, ranges from 0 dB (when frequencies align perfectly) to 1.42 dB (when the analysis frequency is positioned between two lines) The subsequent examples demonstrate that this error can be corrected by summing multiple lines and applying a Hanning correction to the errors.
If all lateral bands are eliminated due to their minimal difference from the mean, resulting in a tone that consists solely of a narrow-band frequency level, \( f_T \), then no Hanning correction is applied to the tone level, \( L_T \).
EXAMPLE 1 The analysis frequency corresponds to the tone frequency.
In Figure A.1 a), the difference \$\Delta\$ between the maximum level and the lateral level is 6 dB, while the difference \$\Delta L\$ between the original tone frequency level and the analyzer value is 0 dB, leading to the following results.
Level of the tone frequency (original and analyzer value): 80 dB
The level of the two lateral lines in the analyzer (80 dB − 6 dB): 74 dB
Level sum without correction: 81,77 dB
The result of the level sum with correction corresponds to the level of the tone frequency.
EXAMPLE 2 The tone frequency lies exactly mid-way between two analysis frequencies.
In Figure A.1 b), the maximum level is split into two lateral levels with a difference of Δ = 0 dB The difference ΔL between the original tone frequency level and the analyzer value is 1.42 dB, leading to the following results.
Original level of the tone frequency distributed over four lateral lines: 80 dB
Of which the two highest (80 dB − 1,42 dB): 78,58
Level sum of the two lateral lines without correction: 81,59 dB
The result of the level sum with correction corresponds approximately to the level of the tone frequency. Figure A.1 is derived from Reference [5] and a brief explanation is given below.
Figure A.1 a) shows three different cases (from left to right):
— the analysis frequency corresponds to the tone frequency;
— the tone frequency (indicated by the dashed line) lies midway between two analysis frequencies;
— the tone frequency (indicated by the dashed line) lies displaced towards the analysis frequency.
The designation B is identical to the line spacing, Δf (see 3.13), of this Publicly Available Specification
In Figure A.1 a), Δf represents the difference between the tone frequency and the analysis frequency: a) in the first case: Δf = 0; b) in the second case: Δf = 0,5 × B; c) in the third case: 0 < Δf < 0,5 × B. a) b)
B line spacing is measured in Hertz (Hz), while Δ represents the difference in decibels (dB) The term ΔL indicates the difference between the actual narrow-band level at the tone frequency, \( f_T \), and the level of the direct lateral band, taking the greater of the two levels in decibels (dB) Additionally, Δf denotes the difference between the tone frequency and the analysis frequency, expressed in Hertz (Hz).
Figure A.1 — Frequency correction and level correction for the Picket fence effect using the
Resolving power of the human ear at frequencies below 1 000 Hz and geometric position of the critical bands — corner frequencies
At frequencies below 1,000 Hz, the human ear can distinguish between tone frequencies that are less than half the width of the critical band when multiple tones are present This ability to detect differences in tones is illustrated by the points or dashed lines in Figure B.1.
— critical bandwidth as a function of frequency [4] ããã noise that comprises two tones
- noise that comprises more than two tones in the critical band under consideration f frequency, in Hertz (Hz) fD frequency difference, in Hertz (Hz)
Figure B.1 — Frequency differences between the tones of complex noises that the human ear can still resolve [6]
Two tones of tone frequencies, fT1 and fT2, are evaluated separately if both tone frequencies lie below
1 000 Hz and the frequency difference, fD: f D = f T 1 − f T 2 (B.1) where fT1, fT2 < 1 000 Hz.
Formula (B.1) exceeds the following value: f f
50 Hz < fT < 1 000 Hz; f T is the frequency of the more pronounced tone, in Hertz (Hz).
The Publicly Available Specification models the critical band as an ideal rectangular filter characterized by a mid-frequency, denoted as \$f_T\$ (tone frequency), along with a lower corner frequency \$f_1\$ and an upper corner frequency \$f_2\$ These corner frequencies are geometrically related to the tone frequency, as referenced in sources [1] and [2], with all frequencies measured in Hertz (Hz) The relationships are defined by the equations \$f_T = \sqrt{f_1 f_2}\$ and \$f_2 = f_1 + \Delta f_c\$.
With the quadratic supplement, it follows from Formula (B.3) and Formula (B.4): f f c f c f
Annex C (informative) Masking, masking threshold, masking index
Masking is the raising of the audibility threshold for a sound as a result of the influence of another sound [3]
The masking threshold, denoted as L ′ T, refers to the sound pressure level of a sinusoidal test tone that must be present for it to be barely detectable amid masking noise, represented by the critical band level, L G This threshold is established through repeated testing, where a group of individuals with normal hearing can perceive the tone in 50% of the trials.
The masking index, defined as \( v = L'_{T} - L_{G} \), represents the difference between the test tone level \( L'_{T} \) and the critical band level \( L_{G} \) At low frequencies, the masking index is approximately \(-2 \, \text{dB}\) However, within a transition range of 0.2 kHz to 1 kHz, it decreases at a constant logarithmic rate, reaching \(-6 \, \text{dB}\) by 20 kHz.
Figure C.1 — Masking index, av, as a function of frequency, f The masking index, a v , is given by Formula (C.1): a f v = − − + Hz dB
2 5 lg / , (C.1) where f is the frequency, in Hertz (Hz).
Annex D (informative) Iterative method for the determination of the audibility, ∆L
Figure D.1 shows an iterative method for calculation of the tonal audibility.
The mean narrow-band level, LS, and auxiliary quantities to determine the uncertainty are calculated for all spectral lines (see Figure D.2).