FINAL REPORT ON THE KEY COMPARISON EUROMET.AUV.A-K3

FINAL REPORT ON THE KEY COMPARISON EUROMET.AUV.A-K3 June 26 CCAUV Approved September 26 ISTITUTO NAZIONALE DI RICERCA METROLOGICA & THE DANISH PRIMARY LABORATORY FOR ACOUSTICS Knud Rasmussen Danish Primary Laboratory for Acoustics Kgs. Lyngby Denmark Tel +45 4525 3937 Fax +45 4588 577 Email: kr@oersted.dtu.dk Claudio Guglielmone INRiM Strada delle Cacce 9, Torino Italy Tel +39 3939626 Fax +39 39962 Email: guglielm@inrim.it /26

Contents Introduction 3. Participants 3 2. Measurement phase 3 3. Stability of the standards 4 4. Results from the laboratories 7 4. Results 7 4.2 Correction for frequency realignment 4.3 Correction for sensitivity drift 2 4.4 Corrected results 3 5. Microphone acoustical impedance 5 6. Analysis of the results 6 6. Linking EUROMET.AUV-K3 to CCAUV.A-K3 6 6.2 Drift of the standards 7 7. Degrees of equivalence 9 8. References 25 Appendix, List of contacts 26 2/26

Introduction The need for a comparison of laboratory standard microphones type LS2aP was agreed during the EUROMET TC AUV Sound in air SC and contact persons meeting in Warsaw, held in May 22. The goal of the comparison is to complement on a regional scale the CCAUV.A-K3 comparison, in order to be able to demonstrate the equivalence of acoustical pressure standards of European NMIs. The EUROMET TC AUV presented a project N 674 for the comparison and it was agreed that IEN would be the pilot laboratory with technical assistance given by DPLA. A Technical Protocol was distributed in September 23 and measurements started in November 23. Draft A was prepared in January 25 and finally approved in May 25 at TC AUV EUROMET meeting in Torino. The CCAUV approved this final report and the degrees of equivalence in September 26.. Participants The following laboratories participated in the comparison: BEV, Austria Metas, Switzerland CEM, Spain Mikes, Finland CMI, Czech Republic NMi, The Netherlands () DPLA, Denmark SP, Sweden IEN, Italy (now INRIM) Contact details are in Appendix () Due to problems in the measuring instruments, NMi withdrew from the comparison 2. Measurements phase Two LS2aP microphones have been circulated for this comparison. They are Brüel & Kjær type 48 microphones serial numbers 395456 and 627783. One of the microphones ( SN 395456 ) changed its sensitivity during a return trip to DPLA and then remained stable in the new sensitivity condition until the end of the comparison. The timetable has been followed without problems but an equipment failure prevented one of the laboratories from performing the measurements in time. The same laboratory was allowed to calibrate the circulating standards at the end of the scheduled period. Unfortunately, new management policies prevented the laboratory to redo the measurements. The laboratory was therefore excluded from the comparison. A more general problem arose form the interpretation of the technical protocol: many laboratories used the exact frequencies and not the standardised nominal octave and third octave frequency values of ISO 266, as required by the protocol. It must be said that the protocol itself could have been more explicit for the frequency selection, and this experience will be useful for the development of new protocols. The frequency mismatch between results of different laboratories creates a problem for obtaining a reference value (for DRAFT A report only) and comparing the results. Fortunately the pilot laboratory calibrated the standards at many more frequencies than those required by the protocol, and some interpolation can be performed. During the elaboration of the Draft A Report, it was decided to interpolate the data at exact frequencies. A similar approach had been adopted for the corresponding CCAUV comparison. 3/26

3. Stability of the standards The standard laboratory microphones used in this comparison are two of the four used in the corresponding CCAUV.A.K-3 comparison, and in the CCAUV comparison they were estimated stable. In this EUROMET comparison one of the microphones drifted in a measurable way. The change in the sensitivity of microphone 48 SN 395456 occurred during the return trip from CEM laboratory. In figure the difference in sensitivity is shown versus frequency. The change was computed on the mean of the calibrations at DPLA before (3 measurements) and after (4 measurements) the change.,3 Sensitivity Drift vs Frequency SN 395456,25 Sensitivity variation /,2,5,,5 -,5 -, 3,5 63 25 25 5 2 4 63 8 25 6 2 25 35 Frequency / Figure. Change in sensitivity of standard microphone SN 395456 as a function of frequency. In figure 2, the drift is shown as a function of time at two frequencies. Only the data of the pilot laboratory are reported. 4/26

Change in sensitivity of standard microphone SN 395456-38.4-38.42 Sensitivity, /Pa -38.44-38.46 25 k -38.48-38.5 5//23 5//23 5/2/23 5//24 5/2/24 5/3/24 5/4/24 5/5/24 Date of measurement Figure 2. Change in sensitivity of standard microphone SN 395456 as a function of time The graph suggests that a sudden change in sensitivity has happened during the circulation, and that the minor variations before March 5 and after the jump are normally related to laboratory repeatability and reversible instabilities of the standard. The difference to the behaviour of microphone SN 627783, reported in figure 3, is evident. This kind of instability is typical of condenser microphones, and reflects a permanent change in some mechanical characteristic of the device (most likely diaphragm tension or distance between it and backplate), triggered by a mechanical or thermal shock. The microphone may then be stable in the new condition, and it is the case that occurred here. The data of this unstable standard can therefore be used, but the approaches used in polynomial approximation of the drift, typical for generalise least squares estimations and suitable for standards like masses, are problematic here. A reasonable proposal is to use the data from the pilot lab, and use the difference shown in figure to correct the data of all measurements after the jump in sensitivity. In the analysis of the results the validity of this approach will be evaluated. 5/26

Change in sensitivity of standard microphone SN 627783-38.7-38.72 Sensitivity, /Pa -38.74-38.76 25 k -38.78-38.8 5//23 5//23 5/2/23 5//24 5/2/24 5/3/24 5/4/24 5/5/24 Date of measurement Figure 3. Change in sensitivity of standard microphone SN 627783 as a function of time 6/26

4. Results from the laboratories 4. Results In the following tables the results of all laboratories and the declared uncertainties are reported. The DPLA results are the first measurements, for model 48 SN 395456 a sensitivity change has been detected. Table I. Results for circulating standard microphone 48 SN 627783 first part DPLA IEN BEV CMI Frequency Sensitivity U95 Frequency Sensitivity U95 Frequency Sensitivity U95 Frequency Sensitivity U95 re re re re 3.5-38.725.8 3.5-38.69.8 3.5-38,72.3 3.62-38.92.8 63-38.736.4 63-38.7.5 63-38,736.3 63. -38.82.6 25-38.752.3 25-38.73.5 25-38,75.2 25.89-38.82.6 25-38.767.3 25-38.74.5 25-38,763.2 25.9-38.8.6 5-38.774.3 5-38.75.5 5-38,77.2 5.9-38.8.6-38.775.3-38.76.5-38,772.2-38.8.6 2-38.75.3 2-38.74.5 2-38,748.2 995.26-38.79.6 4-38.645.3 4-38.63.5 4-38,642.2 398.7-38.69.6 63-38.447.3 63-38.44.5 63-38,444.3 639.57-38.5.7 8-38.273.3 8-38.27.5 8-38,254.4 7943.28-38.36.8-38.78.3-38.7.8-38,7.4-38.7.9 25-37.939.4 25-37.94. 25-37,95.5 2589.25-38.6. 6-38.23.5 6-38.2. 6-38,97.8 5848.92-38.29. 2-39.425.8 2-39.44.5 2-39,394. 9952.63-39.45.7 25-4.72.4 25-4.68.2 25-4,7.4 258.87-4.68.25 35-44.462 7/26

Table II. Results for circulating standard microphone 48 SN 627783 second part Metas CEM Mikes SP Frequency Sensitivity U95 Frequency Sensitivity U95 Frequency Sensitivity U95 Frequency Sensitivity U95 re re re re 3.62-38.684.46 3.62-38.744.5 3.5-38.78.579 3.5-38.73. 63. -38.78.46 63. -38.757.4 63-38.744.284 63-38.72.8 25.89-38.727.38 25.89-38.77.4 25-38.746.258 25-38.732.5 25.9-38.743.36 25.9-38.782.4 25-38.76.258 25-38.744.5 5.9-38.755.36 5.9-38.79.4 5-38.766.283 5-38.752.5-38.759.36-38.792.4-38.769.3-38.75.5 995.26-38.739.36 995.26-38.769.4 2-38.749.442 2-38.729.5 398.7-38.636.34 398.7-38.665.4 4-38.644.432 4-38.623.5 639.57-38.443.32 639.57-38.47.4 63-38.446.437 63-38.427.6 7943.28-38.278.36 7943.28-38.35.4 8-38.275.448 8-38.256.6-38.77.4-38.5.4-38.75.55-38.6.8 2589.25-37.94.45 2589.25-37.97.4 25-37.948.554 25-37.928. 5848.92-38.86.47 5848.92-38.28.5 6-38.27.633 6-38.226.2 9952.63-39.44.63 9952.63-39.48.8 2-39.35.754 2-39.426.2 258.87-4.794.63 258.87-4.76.4 25 25-4.727.3 8/26

Table III. Results for circulating standard microphone 48 SN 395456 first part DPLA IEN BEV CMI Frequency Sensitivity U95 Frequency re Sensitivity re U95 Frequency Sensitivity re U95 Frequency Sensitivity re 3.5-38.367.8 3.5-38.33.8 3.5-38.347.3 3.62-38.39.8 63-38.397.4 63-38.37.5 63-38.38.3 63. -38.42.6 25-38.427.3 25-38.4.5 25-38.49.2 25.89-38.45.6 25-38.45.3 25-38.43.5 25-38.434.2 25.9-38.48.6 5-38.47.3 5-38.45.5 5-38.454.2 5.9-38.5.6-38.482.3-38.47.5-38.466.2-38.5.6 2-38.465.3 2-38.45.5 2-38.447.2 995.26-38.5.6 4-38.34.3 4-38.33.5 4-38.324.2 398.7-38.38.6 63-38.87.3 63-38.8.5 63-38.73.3 639.57-38.4.7 8-37.856.3 8-37.85.5 8-37.825.4 7943.28-37.93.8-37.575.3-37.57.8-37.56.4-37.66.9 25-37.334.4 25-37.34. 25-37.38.5 2589.25-37.44. 6-37.595.5 6-37.59. 6-37.593.8 5848.92-37.66. 2-39.59.8 2-39.9.5 2-39.62.9 9952.63-39..7 25-4.779.4 25-4.78.2 25-4.82.3 258.87-4.85.25 35-44.7 U95 9/26

Table IV. Results for circulating standard microphone 48 SN 395456 second part Frequency Metas CEM Mikes SP Sensitivity U95 Frequency Sensitivity U95 Frequency Sensitivity U95 Frequency Sensitivity U95 re re re re 3.62-38.332.46 3.62-38.365.5 3.5-38.325.579 3.5-38.335. 63. -38.37.46 63. -38.395.4 63-38.348.284 63-38.353.8 25.89-38.42.38 25.89-38.424.4 25-38.377.258 25-38.377.5 25.9-38.43.36 25.9-38.449.4 25-38.44.259 25-38.42.5 5.9-38.453.36 5.9-38.47.4 5-38.426.284 5-38.423.5-38.468.36-38.482.4-38.437.3-38.433.5 995.26-38.452.36 995.26-38.466.4 2-38.49.443 2-38.48.5 398.7-38.33.34 398.7-38.344.4 4-38.295.443 4-38.294.5 639.57-38.79.32 639.57-38.93.4 63-38.4.444 63-38.43.6 7943.28-37.856.36 7943.28-37.87.4 8-37.86.464 8-37.83.6-37.564.4-37.582.4-37.52.535-37.533.8 2589.25-37.322.45 2589.25-37.348.4 25-37.293.59 25-37.38. 5848.92-37.544.47 5848.92-37.579.5 6-37.543.638 6-37.68.2 9952.63-39..63 9952.63-39.23.8 2-38.946.734 2-39.25.2 258.87-4.85.63 258.87-4.9.4 25 25-4.948.3 /26

4.2 Correction for frequency realignment The results of CMI, Metas and CEM must be interpolated to nominal frequencies in order to be used for linking this comparison to the CCAUV one. In the following table the corrections and an estimate of the additional uncertainty due to the standard deviation associated with the determination of the slopes used for the linear interpolation, are reported. It should be noted that the units for uncertainties are thousandth of. Some additional uncertainty should be accounted for at higher frequencies (2 k and 25 k) due to the possibly limited validity of a linear interpolation in that frequency range of the pressure response. The additional uncertainty pertaining to the frequency realignment is negligible compared to the combined uncertainty and will not be accounted for in the following analysis. The correction C is defined as follows: C =[f nom -f exact ]. slope [] where: slope =[(DPLA sensitivity at f nom +/2 octave)- (DPLA sensitivity at f nom -/2 octave)]/ [ ( f nom +/2 octave- ( f nom- /2 octave)] f nom = nominal frequency [] f exact = exact frequency [] Table V. Corrections for frequency realignment From exact Frequency To nominal frequency Correction to nominal frequencies for SN 627783, additional uncertainty -3 Correction to nominal frequencies for SN 395456, additional uncertainty -3 3.62 3.5.7.4.9.6 63. 63.4.3.7.3 25.89 25.8..22. 25.9 25.4.7.9.7 5.9 5.2.2.5.2.... 995.26 2.6..6. 398.7 4.32.2.66.2 639.57 63 -.94. -.25. 7943.28 8.573.8.8.8.... 2589.25 25 -.9.7 -.395.7 5848.92 6 -.275.23 -.322.23 9952.63 2 -.897.22 -.236.22 258.87 25.5568.33.636.33 /26

Table VI. Corrected values for CMI, Metas and CEM. CMI Metas CEM SN SN SN SN SN SN Nominal 395456 627783 395456 627783 395456 627783 re re re re re re V / Pa V / Pa V / Pa V / Pa V / Pa V / Pa 3.5-38.39-38.92-38.332-38.684-38.365-38.744 63-38.42-38.82-38.37-38.78-38.395-38.757 25-38.45-38.82-38.42-38.727-38.424-38.77 25-38.48-38.8-38.43-38.743-38.449-38.782 5-38.5-38.8-38.453-38.755-38.47-38.79-38.5-38.8-38.468-38.759-38.482-38.792 2-38.5-38.79-38.452-38.739-38.466-38.769 4-38.378-38.689-38.329-38.635-38.342-38.664 63-38.4-38.5-38.8-38.444-38.94-38.47 8-37.922-38.354-37.848-38.272-37.862-38.299-37.66-38.7-37.564-38.77-37.582-38.5 25-37.444-38.6-37.326-37.942-37.352-37.97 6-37.692-38.37-37.576-38.23-37.6-38.245 2-39.34-39.469-39.35-39.423-39.47-39.5 25-4.787-4.624-4.788-4.738-4.838-4.66 4.3 Correction for sensitivity drift The drift of microphone B&K 48 SN 395456 has been calculated according to the data in table VII. The mean of four measurements of the pilot laboratory before the sensitivity shift, and of three measurements after the shift have been used to evaluate the difference. The standard deviation of the results of the pilot laboratory is reported, and it is reasonable to assume that no additional uncertainty for this correction needs to be applied. Table VII. Values for the correction of the change of sensitivity of microphone B&K 48 SN 395456 Frequency Drift SD of Pilot Laboratory, 3.5.27.74 63.26.23 25.27.2 25.27.72 5.27..26.25 2.26. 4.25.6 63.23.67 8.23.273.2.299 25.4.49 6.7.462 2 -.4.733 25.6.356 35.2.74 2/26

The correction of the drift has been applied to the results of Mikes and SP, the two laboratories that received the microphones after the sensitivity shift occurred. 4.4 Corrected results In table VIII the results for microphone SN 627783, corrected to nominal frequencies, are reported. Table VIII. Laboratory results for microphone SN 627783 corrected to nominal frequencies. Sensitivity levels, re V / Pa 627783 DPLA IEN BEV CMI Metas CEM Mikes SP Date 5-ott 5-nov 2-nov 3-dic 5-gen -mar 29-mar 28-apr re re re re re re re re 3.5-38.725-38.69-38.72-38.92-38.684-38.744-38.78-38.73 63-38.736-38.7-38.736-38.82-38.78-38.757-38.744-38.72 25-38.752-38.73-38.75-38.82-38.727-38.77-38.746-38.732 25-38.767-38.74-38.763-38.8-38.743-38.782-38.76-38.744 5-38.774-38.75-38.77-38.8-38.755-38.79-38.766-38.752-38.775-38.76-38.772-38.8-38.759-38.792-38.769-38.75 2-38.75-38.74-38.748-38.79-38.739-38.769-38.749-38.729 4-38.645-38.63-38.642-38.689-38.635-38.664-38.644-38.623 63-38.447-38.44-38.444-38.5-38.444-38.47-38.446-38.427 8-38.273-38.27-38.254-38.354-38.272-38.299-38.275-38.256-38.78-38.7-38.7-38.7-38.77-38.5-38.75-38.6 25-37.939-37.94-37.95-38.6-37.942-37.97-37.948-37.928 6-38.23-38.2-38.97-38.37-38.23-38.245-38.27-38.226 2-39.425-39.44-39.394-39.469-39.423-39.5-39.35-39.426 25-4.72-4.68-4.7-4.624-4.738-4.66-4.727 3/26

In table IX, the results for microphone SN 395456, corrected to nominal frequencies, and for sensitivity level drift (Mikes and SP laboratories only) are reported. Table IX. Laboratory results for microphone SN 395456 corrected to nominal frequencies and for sensitivity level drift. Sensitivity levels, re V / Pa 395456 DPLA IEN BEV CMI Metas CEM Mikes SP Date 5-ott 5-nov 2-nov 3-dic 5-gen -mar 29-mar 28-apr re re re re re re re re 3.5-38.367-38.33-38.347-38.39-38.332-38.365-38.352-38.362 63-38.397-38.37-38.38-38.42-38.37-38.395-38.374-38.379 25-38.427-38.4-38.49-38.45-38.42-38.424-38.44-38.44 25-38.45-38.43-38.434-38.48-38.43-38.449-38.43-38.429 5-38.47-38.45-38.454-38.5-38.453-38.47-38.453-38.45-38.482-38.47-38.466-38.5-38.468-38.482-38.463-38.459 2-38.465-38.45-38.447-38.5-38.452-38.466-38.445-38.444 4-38.34-38.33-38.324-38.378-38.329-38.342-38.32-38.39 63-38.87-38.8-38.73-38.4-38.8-38.94-38.63-38.66 8-37.856-37.85-37.825-37.922-37.848-37.862-37.829-37.836-37.575-37.57-37.56-37.66-37.564-37.582-37.54-37.553 25-37.334-37.34-37.38-37.444-37.326-37.352-37.37-37.322 6-37.595-37.59-37.593-37.692-37.576-37.6-37.55-37.65 2-39.59-39.9-39.62-39.34-39.35-39.47-38.942-39.2 25-4.779-4.78-4.82-4.787-4.788-4.838-4.954 4/26

5. Microphone acoustical impedance Microphone parameters used in the calculations are reported in table X. A rather good agreement is shown, but the comparison was not intended to examine this aspect of microphone calibration and the data are reported for information only. 48 SN 627783 Table X. Results of the measurements of microphone electro mechanical parameters. DPLA CMI CEM BEV Metas SP Mikes IEN Mean Front cavity volume mm 3 3.7 3.657 3.2 32 3.9 3.6 3.6 3.7 3.353.6772 Cavity depth mm.469.46.455.46.49.47.45473.46.465.7 Equivalent Volume mm 3 8.5 9.3 8.6 9 8.55 9.9 9 8.8 8.868.39 Resonance frequency k 22.7 22.5 22 22.5 22.2 22 2.84 2.2 2.92.8375 Loss factor.5.5.5.5.6.5.8.7.7.342 48 SN 395456 SD Front cavity volume mm 3 34.6 33.53 34.9 35.5 34.32 35.5 34.55 34.73 34.7.647 Cavity depth mm.54.54.58.55.477.54.55.57.52. Equivalent Volume mm 3 9.3 9.3 8.4 9.2 9.7 9.9 9.4 9.4 9.236.374 Resonance frequency k 2.2 22.5 22 2 22.8 22 9.6 2.6 2.33.923 Loss factor.98.5.5.6.5.96.3.4.52 5/26

6. Analysis of the results 6. Linking EUROMET.AUV.A-K3 to CCAUV.A-K3 A regional comparison should not try to calculate a key comparison reference value (KCRV), unless for internal purposes []. In Draft A Report for EUROMET.AUV.A-K3 comparison, such an attempt was made and the un-weighted mean and the median were used as estimators [2]. The method chosen for calculating the degrees of equivalence of the laboratories in this report is the generalized least square method, as suggested in point 9 of reference []. This choice has two main reasons: ) There are two travelling standards, one likely drifting; 2) A method based on the generalized least squares approach has been applied in the analysis of the corresponding CCAUV.A-K3 comparison. The approach used in this analysis of the results is the method proposed by reference [3] for linking international comparisons. But as noted in paragraph 3, the drift, or more appropriately jump, in sensitivity of one of the standards, has been dealt with in a different way. The model used in reference [3] can be expressed in the form: y = Xβ + e () where: y = (y..y g ) T is a column vector of the results X is the design matrix g h β = (βi.β h ) t is a column vector of the unknowns e =(e.e g ) is a vector of random errors or disturbances. Each row of X, except the last, represents one of the comparison measurements (EUROMET or CCAUV, 28 + in the present case), and there is a corresponding result in the vector y. The last row of X and the last value of y are related to the constraint. In reference [3] it is shown that the approximationβˆ ~ of best linear unbiased estimate β can be expressed as: β ˆ T = CX ˆ Φ y (2) where Cˆ is the uncertainty matrix defined as: ˆ T C = ( X Φ X) The matrix Φˆ is a symmetric g g matrix, whose diagonal elements are the variances associated with each measurement result (standard uncertainty squared). Off diagonal elements allow for correlation between measurements, in our case, following the analysis of the CCAUV.A-K3 comparison, a correlation coefficient of,7 was chosen for measurements made by the same laboratory, while measurements of different laboratories were considered essentially uncorrelated. In the following, standard will designate microphone B&K 48 SN 627783, and standard 2 microphone B&K 48 SN 395456. The result vector y is formed as follows: y y 8 are the measurements results on travelling standard in EUROMET.AUV-K3; y 9 y 6 are the measurements results on travelling standard 2 in EUROMET.AUV-K3; y 7 is the deviation of DPLA from KCRV as determined in CCAUV.A-K3; y 8 is the constraint, difference from KCRV is forced to. The design matrix X has the form: (3) 6/26

= X Columns to 8 are relative to the eight laboratories that took part in the comparison, columns 9 and are for the two standards, in any case no local reference value is needed. Column is for the link. Rows to 8 are relative to the 8 measurements on standard, rows 9 to 6 are relative to measurements on standard 2. The last two rows are for the link (deviation of linking laboratory from CCAUV KCRV) and for the constraint. One the laboratories did not provide a result at 25 k, therefore at 25 k has columns instead of and 6 rows instead of 8. X The degrees of equivalence are calculated from β and. The deviations are obtained from β β 8 and the uncertainty U i of the deviations are: Ĉ ˆ ii i k U Ĉ = (4) where k is the coverage factor, it has been assumed k=2. 6.2 Drift of the standards The change of the sensitivity of one of the microphones was clearly visible in a preliminary analysis of the data. An attempt has been made to model the drift of the standards with a polynomial model, according to reference [3]. The sensitivity s of the microphone i is expressed as a function of time t as: 3 2 ' ) ( t c b t t a s t s i i i i i + + + = (5) In the design matrix three columns for standard, with t, t 2 and t 3 and three columns for standard 2 are added, on the rows relative to the respective measurements. The time t reflects the measurements date, as the X 7/26

spacing of the measurements in this comparison is not constant. The analysis included all measurements from the pilot laboratory only, for a total of 4 results and X in this case has 6 rows. In figures 4 and 5 the behaviour of the two standard microphones, calculated according to (5), without any a priori correction for the drift is reported..4.3.2 drift /. -. -.2 5//3 5//3 5/2/3 5//4 5/2/4 5/3/4 5/4/4 5/5/4 Date of measurement 3.5 25 2 Figure 4. Drift of microphone B&K 48 SN 627783 during the comparison: polynomial fit..4.3.2 drift /. -. -.2 5//3 5//3 5/2/3 5//4 5/2/4 5/3/4 5/4/4 5/5/4 Date of measurement 3.5 25 2 Figure 5. Drift of microphone B&K 48 SN 395456 during the comparison: polynomial fit, no correction applied to data. In figure 6, the data for microphone B&K 48 SN 395456, calculated on the measurement data corrected for the shift in sensitivity as described in 4.3, is reported. 8/26

.4.3.2 drift /. -. -.2 5//3 5//3 5/2/3 5//4 5/2/4 5/3/4 5/4/4 5/5/4 Date of measurement 3.5 25 2 Figure 6. Drift of microphone B&K 48 SN 395456 during the comparison: polynomial fit, correction applied to data. The comparison of figure 5 and figure 6 shows that the applied correction as reported in figure 6 seems to work well, while the polynomial fit in figure 5 is not able to follow the shift in sensitivity accurately. It is in fact reasonable to assume that, given the typical behaviour of standard laboratory microphones, the sensitivity change is essentially a step function, and a polynomial function of degree 3 is not able to follow it accurately. 7. Degrees of equivalence The degrees of equivalence have been calculated from (2) and (3) for deviations and their uncertainties respectively. The data from CCAUV.A.K3 Draft B report [4] have been used for the calculations. In particular, the deviations of the linking laboratory, DPLA, and their uncertainty from the KCRV were used in the calculations. In table XI the deviations of the measurements, directly derived from β ˆ after solving equation (2) are reported. The same data is reported in graphical form in figure 7. In table XII are reported the uncertainties of the deviations of table XI, derived from the diagonal elements of Ĉ with a coverage factor of 2. The inter laboratory degrees of equivalence are reported for the frequencies of 25 and in tables XIII to XVI. The data are calculated from βˆ. The deviation of laboratory i from laboratory j is: D i, j = β β i j i, j Ĉ D i, j and its uncertainty U is again obtained from using the formula: (4) U 2C i, j = k Cii + C jj ij where k is the coverage factor, it has been assumed k = 2. (5) 9/26

Table XI. Degrees of equivalence per laboratory and per frequency: deviations, expressed in. DPLA IEN BEV CMI Metas CEM Mikes SP Deviations, 3.5 -.5.3.7 -.4.33 -.3 -.25.3 63 -.2.24.6 -.56.25 -.2.5.5 25 -.3.22.7 -.48.23 -..2.9 25 -.4.2.6 -.4.8 -..9.8 5 -.4.9.6 -.36.5 -..9.8 -.4..6 -.35. -.2.9.2 2 -.4..7 -.4.9 -.3.8.8 4 -.3.9.6 -.44.7 -.4.7.8 63..7.9 -.59.5 -.5.3.2 8 -.2.2.23 -.76.2 -.8..6 -.3.4.8 -.9.3 -.2.7.8 25. -.4.2 -.6.2 -.25.9.2 6..8.8 -.9.9 -.5.35 -.7 2.5 -.8.29 -.44.28 -.66. -.7 25 -.2.8 -.3.42 -.5 -. - -.93 2/26

Table XII. Degrees of equivalence per laboratory and per frequency: uncertainties of the deviations, expressed in. DPLA IEN BEV CMI Metas CEM Mikes SP Uncertainty, 3.5.82.93.63.93.7.73.78.8 63.42.55.4.63.52.47.4.8 25.32.52.3.6.42.44.33.52 25.32.52.3.6.4.44.33.52 5.32.52.3.6.4.44.35.52.32.52.3.6.4.44.36.52 2.32.52.3.6.4.44.47.52 4.32.52.3.6.39.44.46.52 63.33.52.37.69.38.44.47.6 8.33.52.44.78.4.44.48.6.34.78.45.87.46.45.53.78 25.44.98.57.98.53.49.6.98 6.55..85..6.62.7.8 2.88.53.3.7.87.98.95.95 25.52.25.7.256..7 -.298 2/26

.5..5 Deviation / -.5 -. -.5 Frequency / DPLA IEN BEV CMI Metas CEM Mikes SP Figure 7. Deviations from KCRV as a function of frequency. 22/26

Table XIII. Inter laboratory degrees of equivalence at 25, deviations 25 DPLA IEN BEV CMI Metas CEM Mikes SP DPLA - -.24 -..36 -.22.7 -.3 -.22 IEN.24 -.4.6..3..2 BEV. -.4 -.46 -.2.7 -.3 -.2 CMI -.36 -.6 -.46 - -.58 -.3 -.49 -.58 Metas.22 -..2.58 -.29.9. CEM -.7 -.3 -.7.3 -.29 - -.2 -.29 Mikes.3 -..3.49 -.9.2 - -.9 SP.22 -.2.2.58..29.9 - Table XIV. Inter laboratory degrees of equivalence at 25, uncertainty 25 DPLA IEN BEV CMI Metas CEM Mikes SP DPLA -.54.33.62.43.46.36.54 IEN.54 -.5.72.57.59.52.65 BEV.33.5 -.58.38.4.3.5 CMI.62.72.58 -.65.66.6.72 Metas.43.57.38.65 -.5.4.57 CEM.46.59.4.66.5 -.44.59 Mikes.36.52.3.6.4.44 -.52 SP.54.65.5.72.57.59.52 - Table XV. Inter laboratory degrees of equivalence at, deviations k DPLA IEN BEV CMI Metas CEM Mikes SP DPLA - -.4 -..3 -.5.8 -.3 -.24 IEN.4 -.4.45 -..22. -. BEV. -.4 -.4 -.6.8 -.3 -.4 CMI -.3 -.45 -.4 - -.47 -.23 -.44 -.55 Metas.5..6.47 -.23.2 -.9 CEM -.8 -.22 -.8.23 -.23 - -.2 -.32 Mikes.3 -..3.44 -.2.2 - -. SP.24..4.55.9.32. - Table XVI. Inter laboratory degrees of equivalence at, uncertainties k DPLA IEN BEV CMI Metas CEM Mikes SP DPLA -.54.33.62.43.46.39.54 IEN.54 -.5.72.57.59.54.65 BEV.33.5 -.58.38.4.33.5 CMI.62.72.58 -.65.66.62.72 Metas.43.57.38.65 -.5.43.57 CEM.46.59.4.66.5 -.46.59 Mikes.39.54.33.62.43.46 -.54 SP.54.65.5.72.57.59.54-23/26

8. References [] Brief guidelines for linking RMO key comparisons to the CIPM KCRV. CCAUV/4-27, BIPM 26 May 24 [2] DRAFT A REPORT EUROMET.AUV.A-K3, January 25 [3] C.M. Sutton. Analysis and linking of international measurement comparison. Metrologia 4 (24) 272-277. [4] V. Cutanda Henriquez, K. Rasmussen. Report on the Key Comparison CCAUV.A-K3 Draft B. January 26 24/26

Appendix List of contact persons BEV: IEN: Merita Sinojmeri Claudio Guglielmone BEV Istituto Elettrotecnico Nazionale (IEN) Department: Acoustics, frequency, time Galileo Ferraris Arltgasse 35 Strada Delle Cacce 9 6 Wien I-35 Torino Austria Italy Tel: +43 49 39 Tel: +39 399 626 Fax: +43 4928 875 Fax: +39 346 384 E-mail: m.sinojmeri@metrologie.at E-mail: guglielm@ien.it CEM: METAS: Carmen Casal Sobrino Centro Espanol de Metrologia (CEM) At time of the comparison: Department: Laboratorio de Acustica Fabienne Berthod Calle Del Alfar 2 Swiss Federal Office of Metrology & Accreditation (METAS) 2876 Tres Cantos Lindenweg 5 Madrid 33 Bern-Wabern Spain Switzerland Bus: +34 9 87 4825 Tel: +4 3 32 34 75 Bus Fax: +34 9 87 487 Fax: +4 3 32 33 2 E-mail: ccasal@cem.es E-mail: fabienne.berthod@metas.ch Now : Dr. Christian Hof Tel: + 4 3 32 34 75 Fax: +4 3 32 33 2 E-mail: christian.hof@metas.ch CMI: MIKES: Michal Bartos Kari Ojasalo Czech Metrology Institute (CMI) Centre for Metrology and Accreditation (MIKES) V Botanice 4 Department: Electricity Group 572 Praha 5 P.O. Box 9 (Tekniikantie ) The Czech Republic 25 Espoo Finland Tel: +42 2 573 46 9 Fax: +42 2 5732 8 77 Tel: +358 654 423 E-mail: mbartos@cmi.cz Fax: + 358 654 498 E-mail: kari.ojasalo@mikes.fi DPLA: NMI: Knud Rasmussen Paul van Kan Danish Primary Laboratory of Acoustics Nederlands Meetinstituut (NMi) Acoustic Technology Postbus 654 Oersted Institute, DTU Schoemakerstraat 97 Building 352 26 AR Delft 28 Kgs. Lyngby The Netherlands Denmark Tel: + 3 52 69 673 Tel: +45 4525 3937 Fax: + 3 52 62 97 Fax: +45 4588 577 E-mail: pvankan@nmi.nl Email: kr@oersted.dtu.dk 25/26

SP: Hakan Andersson Swedish National Testing & Research Institute (SP) PO Box 857 SE-55 Boras Sweden Tel: +46 33 6 54 23 Fax: +46 33 3 83 8 E-mail: hakan.andersson@sp.se 26/26