Reverberation time and structure loss factor CHRISTER HEED SD2165 Stockholm October 2008
Marcus Wallenberg Laboratoriet för Ljud- och Vibrationsforskning Reverberation time and structure loss factor Christer Heed Approved Date: Signature: SD2165 Acoustical measurements
ABSTRACT Reverberation time measurements are useful both in acoustics and in vibration. Reverberation time in third octave band of two samples is to be measured: A test room and a thin (1 mm) steel plate. The standard ISO: 354:2003 is followed where applicable. The reverberation time and absorption of the room and the structure loss factor of the plate are calculated. The reverberation time of the room is around 0.4 s and the room absorption becomes 70 m 2 which is 36 % of the room s area. Compared to an earlier measurement [1], where the absorption was estimated, the absorption is much higher. The structure loss factor of the steel plate is calculated to ~10-4, which is relatively near the real value. Compared to an earlier measurement [2], where the structural loss factor was a factor 10 to low, this measurement method is better.
TABLE OF CONTENTS 1 INTRODUCTION...1 1-1 Task...1 1-2 Test samples...1 2 MEASUREMENTS...2 2-1 Measurement environment...2 2-2 Instrumentation...2 2-3 Data acquisition and settings...3 2-4 Measurement procedure...3 2-4-1 Reverberation time of the test room...3 2-4-2 Reverberation time of the test structure...4 3 RESULTS...4 3-1 Reverberation time and absorption of the test room...4 3-2 Loss factor of the test structure...5 4 DISCUSSION...5 5 REFERENCES...6 6 APPENDIX...6
1 INTRODUCTION 1-1 Task The task is to measure reverberation time of a test room and then calculate the absorption of the room. It is also to measure structural loss factor by using reverberation time method. 1-2 Test samples The test samples used to do these measurements are test room MWL 75 and a steel plate with 1 mm thickness which is hung up with strings attached at the corners, the left plate in figure 1. Figure 1: The 1 mm steel plate to the left. It is hung up in strings. The left string is twined. The properties of the test samples are as follows: 1 mm steel plate 500 mm 600 mm o Density (approx.): 7800 kg/m 3 Test room is the MWL 75 room of KTH o Dimensions (L W H): 6.7 m 6 m 4.5 m Air volume: 180.9 m 3 (approx.) Surface area: 194.7 m 2 (approx.) 1
2 MEASUREMENTS 2-1 Measurement environment The environmental data and date are as follows: Measure location: Room MWL 75, KTH in Stockholm Sweden o Dimensions (L W H): 6.7 m 6 m 4.5 m Date: 7 October 2008 Air temperature: Not checked Relative humidity: Not checked 2-2 Instrumentation The following equipment is used for the measurements: PC with sound card and Microsoft Windows and Excel Data recording software: Matlab Data processing software: Matlab Octave filter set: Brüel & Kjaer type 1613 o Serial No.: 326229 Additional equipment used for the room reverberation measurement: o Signal generator: Brüel & Kjaer type 1405 Serial No.: 904206 o Band pass filter set: Brüel & Kjaer type 1625 Serial No.: 424121 o Power amplifier: Zachry D250 Serial No.: 614142 o Sound source: Omni directional loudspeaker 1 Brüel & Kjaer 1 (made by) Kent L. o Microphone: MK224 PCP233/15 Serial No.: 951246 o 2 Preamplifier: MWL-UNO 06 Additional equipment used for the loss factor measurement: o Accelerometer: Brüel & Kjaer type 4393V Serial No.: 1929298 o Charge amplifier: Brüel & Kjaer type 2635 Serial No.: 669742 The Excitation system for the reverberation time measurement is as follows: The signal generator with preamplifier is connected via the band pass filter set to the power amplifier to which the sound sources are parallel coupled. The receiving system is as follows: The microphone with preamplifier is connected via the octave filter set to the sound card of the PC. The receiving system for loss factor measurement is as follows: The accelerometer is connected to the input of the charge amplifier whose output is connected to the octave filter set which is connected to the input of the sound card of the PC. The sensitivity of the accelerometer is of less importance since we are interested in the slope of the decay curve, figure 2. 2
2-3 Data acquisition and settings A PC with Matlab is used for all measurements and calculations of the reverberation time. The sampling frequency that is used is 11025 Hz in order to cover the 5 khz band and to reduce the amount of data. The measurement time is adjusted to cover at least one decaying curve. Refer to page 128 in [3] for the Matlab code and further settings that are used. 2-4 Measurement procedure The reverberation time measurements are performed in one third octave bands from 100 Hz up to 5 khz with band-limited white noise as excitation source. To save time only the bands with centre frequency 125, 250, 500, 1000, 2000 and 4000 Hz are measured. The calculations of the reverberation time are made by the least-square method and the code used is the one on page 129 in [3] to fit the data to a straight line. A graphical input is used to locate the start and end points of the data range. The time for 30 db decay of the sound pressure level is enough to get the reverberation time. The straight line fitted by the linear regression is then plotted in black by the program, as in the example in figure 2. The red line is from the use of ones eye, which is close to the method people used before 1990 [3]. The corresponding reverberation time is then calculated by the program. The value obtained via least-square-fit method is recorded. The eye obtained value is for reference only. Figure 2: The graphical input in Matlab where the decaying curve is presented. The red line is from the use of ones eye and the black is the straight line fitted by the linear regression. 2-4-1 Reverberation time of the test room The sound sources and microphone are positioned appropriately according to [3]. Matlab is started and the filter is set to one third octave band with centre frequency 500 Hz. The signal generator is set to white noise and is then started. The loudspeakers are now producing noise at 500 Hz band. Due to the fact that the dynamic of the room is too low, the two lowest bands are omitted. Two omni directional loudspeakers are used to get high enough sound level, but for the 4000 Hz band it is enough to excite the room with only one speaker. The recording is started in Matlab and the signal is turned off. When the echoes in the room have died away it is turned on again. This is repeated till three decay curves are recorded. Now the above curve fitting procedure starts and data is stored. The 3
measurements are repeated for all above mentioned frequency bands, and further more, according to the standard (ISO 354:2003), the number of spatially independently measured decay curves should be at least 12. To save time only three combinations of microphone and sound source position are used. At 2000 Hz only two combinations are used due to the fact that the results are more stable. The averaged reverberation time and the calculated absorption are presented in table 1, section 3-1. 2-4-2 Reverberation time of the test structure The test sample (1 mm steel panel) is hung up in two strings at the upper corners according to figure 1. One of the strings is twined which should make the structure more damped and influence the reverberation time. The same method as before is used, but with the difference that the vibrations are picked up with an accelerometer, and since this is a light-damped structure, impulse excitation is needed. This is done by knocking the structure with frequency adaptable articles, that is, in order to have high enough vibration acceleration level of the structure at the interested frequency band without overloading the system, harder and lighter hammers are used for higher frequencies. The advantage of this method compared to the use of a shaker is that the shaker is damping the structure which introduces errors. Measurement time is reduced for higher frequencies. At least three averaged measurements of each frequency band are recorded in Matlab and with curve fitting method as described in section 2-4. The bare hand i.e. finger tip and nail are used to excite the three lowest frequency bands. The 1 and 2 khz bands are excited with two different types of keys and the high 4 khz band is exited by the use of a 0.5 mm steel tip of a pen. The averaged reverberation time and the calculated structure loss factor are presented in table 2, section 3-2. 3 RESULTS 3-1 Reverberation time and absorption of the test room Table 1 shows the averaged reverberation time (which is near 0.4 s) and absorption of the test room. The absorption of the test room is calculated from the formula: 55.3V A= 4Vm, where V is the volume of the test room, c is the speed of sound in the ct air and T is the reverberation time, measured in section 2-4-1. The air absorption coefficient m is omitted in this calculation. In an earlier measurement [1], the value of the absorption was estimated to 48.7 m 2 from the approximate value of mean absorption coefficient of the test room suggested by the standard ISO 3746 as 0.25. Centre frequency (Hz) Absorption (m 2 ) Average reverberation time (s) 500 64.2 0.459 1000 80.0 0.368 2000 70.9 0.415 4000 69.5 0.423 Table 1: The reverberation time of the test room and its absorption of the test room presented in selected third octave band. 4
3-2 Loss factor of the test structure 2.2 The structural loss factor of the 1 mm plate is calculated using the formula: η =, ft where f is the centre frequency in third octave band and T is the corresponding reverberation time measured in section 2-4-2. The structural loss factor is expressed in selected third octave band and presented in table 2. The values are relatively near the material loss factor ~10-4. Centre frequency (Hz) Loss factor (1) Average reverberation time (s) 125 0.000871 20.20 250 0.000708 12.42 500 0.000458 9.617 1000 0.000223 9.871 2000 0.000176 6.244 4000 0.000141 3.892 Table 2: Structural loss factor of the steel plate calculated from measurements with reverberation time method. 4 DISCUSSION In an earlier measurement [1], the value of the absorption of the test room was estimated to 48.7 m 2. This time the absorption is calculated to 70 m 2 (the value is from the higher frequency bands, where the measurement was more stable). Compare these results to 195 m 2 which is the approximate total surface of the room. The estimated absorption does not take into account that there are people in the room during measurement and that the surface area of the room is possibly to low (since it did not consider the area of furniture and equipment). The high measured absorption of the room is due to the facts that there were approximately 10 people absorbing high frequencies in the room during measurement and that the approximate value of the air volume is too high since it is not reduced by the volume of the people, furniture and equipment. Also, the power attenuation coefficient of the air is omitted. The structure loss factor for a 3 mm steel plate (otherwise the same dimensions) was measured earlier [2]. That method yields the loss factor ~10-3 and the reverberation time method yields the loss factor ~10-4 which is nearer the real loss factor of steel. The weight of the accelerometer compared to the weight of the structure is higher for this measurement since the structure is thinner and consequently lighter and this could influence the structural damping. The twined string is damping the structure somewhat more than if it is not twined. If elastic strings are used to hang the structure instead, the influence from the support is decreased. The excitation method for the reverberation time measuring method does not introduce such errors that the heavy damping shaker does. As can be seen in table 2, the loss factor is decreasing for higher frequencies when it should be roughly constant with frequencies. This indicates that the averaging time has not been changed often enough and that it could be depending on structural damping. The latter is especially for high frequencies since the reverberation time might be too short. The reverberation time method might also have some problems when the slope of decay (which might not be straight) should be determined. The damping of the structure is mode dependent so the modal density in the interesting frequency range might not be high enough. This means that the measured loss factor for a certain frequency band is the loss 5
factor for the specific mode of the structure rather than the loss factor of the material. To measure the loss factor of the material only, a simple shape is preferred, for example a beam. When damping of low value (< 10-4 ) or very low weight structure is going to be measured, the radiation loss factor has to be taken into account [3]. The conclusion is however that the reverberation time method works better than the power injection method to determine the loss factor of light and thin structures. To get higher structural loss factors one could use a joint. An extra exercise is done measuring the structure loss factor of a jointed steel plate. The joint raises the structural loss factor 10 times. Further details refer to the appendix. 5 REFERENCES [1]: Christer Heed, Sound power measurements, SD2165, October 2008 [2]: Christer Heed, Basic vibration measurements and structure loss factor with power injection method, SD2165, October 2008 [3]: Leping Feng, Acoustical measurements, Lecture notes, TRITA-AVE 2007:07, ISSN 1651-7660, 2 nd print (2008) 6 APPENDIX An extra exercise is done measuring loss factor of another type of plate with the same dimensions and the same method as the previous one, figure 3. This plate is jointed and is far more damped since the joint has the same effect as using an additional mass. The reverberation time at 1000 Hz is 0.75 s and the structure loss factor is thus ~0.003. Figure 3: The structure loss factor of two jointed plates is measured as an extra exercise. 6