MMAN9325 LAB 2

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Oct 30, 2023

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MECH9325 Laboratory 2 – Measurement of Sound Power Anthony Ngo-Le, z5312271 Submission date: 25/07/2023 By submitting this work, I acknowledge that the intellectual content of this report is my own, except where the contributions of others are explicitly described and/or properly cited. I am familiar with my responsibilities under the UNSW Student Code and understand how UNSW defines plagiarism and academic integrity.

Table of Contents 1. Introduction ....................................................................................................................................... 1 2. Procedure .......................................................................................................................................... 1 2.1 Direct method .............................................................................................................................. 2 2.2 Comparison method .................................................................................................................... 2 3. Results ............................................................................................................................................... 3 3.1 Direct method results .................................................................................................................. 3 3.2 Comparison method results ......................................................................................................... 3 3.3 Comparison of direct method and comparison method .............................................................. 4 4. Discussion .......................................................................................................................................... 4 5. Summary ........................................................................................................................................... 4 References ............................................................................................................................................. 5 Table of Figures Figure 1: Microphone positions on the hemispherical measurement surface for a broadband noise source [1] ............................................................................................................................................... 1 Figure 2: Graph showing the relationship between the average SPL of the drill vs. the octave band centre frequency .................................................................................................................................... 4 Table of Table Table 1: The averaged measured sound pressure location across 10 locations .................................... 3 Table 2: Data calculated using the direct method to find sound power level of the electric drill .......... 3 Table 3: Data calculated using the comparison method to find sound power level of the electric drill.3 i

1. Introduction The objective of this laboratory is to evaluate the sound power levels of a noise source, that source being an electric drill. The laboratory will be completed using a common engineering method which is used for essentially free fields near a reflecting plane. The testing can be conducted in a semi-reverberant field such as a large, spacious room or near a hard ground surface if testing outdoors. Further elaboration of the engineering method applied can be found in Australian Standard AS 5335:2019, which details how to correctly compute an environmental correction for reverberation effects. The method itself is comprised of two different approaches: the direct method and the comparison method. 2. Procedure The octave sound pressure level (SPL) of an electric drill was measured at 10 different locations within a hemispherical surface with a radius of 1 m. Figure 1: Microphone positions on the hemispherical measurement surface for a broadband noise source [ CITATION Kes \l 3081 ] To determine the average measured sound pressure level at each octave band centre frequency (L p(S) ), the following equation was applied, ´ L p ( S ) = 10log 10 ( 1 N ∑ i = 1 N 10 L pi 10 ) Where i = 1: N ( N = 10 ) . Subsequently, the sound power level of the noise source was calculated through either the direct method or the comparison method. The result for each octave band centre frequency was then unweighted, as the original SPL measured was A- weighted previously.

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2.1 Direct Method The direct approach compensates for the fact that the environment is not a truly free field and as such, still contains minor reverberation effects. To accomplish this, an environmental correction factor K 2 is subtracted from the average measured sound pressure level. K 2 can be computed by first calculated the equivalent sound absorption area A . A = 0.16 V T 60 Where V is the volume of the room in m 3 , which can be calculated to be 208.656 m 3 using the dimensions given. T 60 is the reverberation time and can be calculated using the linear extrapolation formula. y = y 1 + ( x − x 1 )( y 2 − y 1 ) ( x 2 − x 1 ) T 60 = T 20 + ( 60 − 20 ) ( T 30 − T 20 ) ( 30 − 20 ) The average T 60 was calculated over three measurements for each octave band centre frequency. The environmental correction can then be found, K 2 = 10log 10 ( 1 + 4 S A ) S refers to the area of the enclosed hemispherical surface, which is equivalent to 2 π m 2 . Upon finding the environmental correction factor, the corrected sound pressure level ´ L p can be deduced, ´ L p = ´ L p ( S ) − K 2 Knowing that S o = 1 m 2 , L W = ´ L p + 10log 10 S S o This series of calculations are performed for each octave band. 2.2 Comparison Method A B&K Reference Sound Type 4202 was placed next to an electric drill from the start of the electric drill’s operating time. The reference sound source was switched on and octave band sound pressure level measurements were taken at the same 10 locations. Using the average sound pressure level calculated previously, the uncorrected sound power level (L w (uncorrected) ) can be found, L W ( uncorrected ) = ´ L p ( S ) + 10log 10 S S o The environment correction factor, K 2 , can then be derived, K 2 = L W ( uncorrected ) − L W ( RSS ) L W (RSS) refers to the octave sound power levels of the calibrated reference sound source which can be found in the product data provided by the manufacturer.

3. Results All results are to 3 significant figures. Table 1: The averaged measured sound pressure location across 10 locations 125 Hz 250 Hz 500 Hz 1000 Hz 2000 Hz 4000 Hz 8000 Hz L p(S) (dB) 36.4 52.9 55.8 56.8 61.5 60.2 57.1 3.1 Direct Method Results Table 2: Data calculated using the direct method to find sound power level of the electric drill. 125 Hz 250 Hz 500 Hz 1000 Hz 2000 Hz 4000 Hz 8000 Hz T 60 (average) (s) 3.64 1.41 1.18 1.03 0.883 0.793 0.697 A (m 2 ) 9.16 23.6 28.4 32.4 37.8 42.1 47.9 K 2 5.73 3.15 2.75 2.49 2.21 2.03 1.83 L P (dB) 30.6 49.8 53.0 54.3 58.1 57.2 56.4 L W (dB) 38.6 57.7 61.0 62.3 66.2 65.1 64.4 L W overall (dB) 71.4 3.2 Comparison Method Results Table 3: Data calculated using the comparison method to find sound power level of the electric drill. 125 Hz 250 Hz 500 Hz 1000 Hz 2000 Hz 4000 Hz 8000 Hz L W (uncorrected) (dB) 44.3 60.9 63.8 64.8 69.6 68.2 65.1 L w (RSS) (dB) 80.5 82.4 82.6 87.1 86.9 84.1 80.7 K 2 -36.2 -21.5 -18.8 -22.3 -17.3 -15.9 -15.6 L W overall (dB) 74.1

3.3 Comparison of direct method and comparison method 125 250 500 1000 2000 4000 8000 0 10 20 30 40 50 60 70 80 Average sound power level of the electric drill for each octave band centre frequency LW (Comparison) LW (Direct) Octave band centre freqency (Hz) Sound power level (dB) Figure 2: Graph showing the relationship between the average SPL of the drill vs. the octave band centre frequency. 4. Discussion From the results, it can be observed that the values of L w produced by each method differ only slightly. The value of L w as computed by the direct method was 71.4 dB whereas the value of L w for the comparison method was 74.1 dB. Furthermore, from Figure 2, across each octave band centre frequency, both methods synthesised a similar trend. As such, it can be inferred that both methods are valid and reliable in calculating the sound power level of an unknown sound source and in calculating the overall sound power level of the source. Advantages of the direct method when compared to the comparison method is that it produces more accurate results as the sound emitted by the source is directly captured by the equipment. In addition to this it is more suitable for complex sources but can be time- consuming and expensive to set up. On the other hand, the comparison method is generally easier, less time consuming, and less expensive to set up, but it results in less accuracy. Moreover, it can be difficult finding a suitable reference source especially for a more complex or large sound source[ CITATION Hak10 \l 3081 ]. 5. Summary The laboratory examined two methods utilised in calculating the sound power level of an unknown source, these being the direct method and the comparison method. Both methods recorded similar results across each individual octave band centre frequency as well as a similar overall sound power level. Although these methods can be used interchangeably when determining sound power level of a source, the direct method is more effective in doing so. This is due to its high accuracy and ability to analyse even the most complex sound sources when compared to the comparison method.

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References [1] N. Kessissoglou, “Fundamentals of Acoustics and Noise Unit 4 Measurement of Sound Power,” UNSW. [2] C. Hak, R. H. J. Wenmaekers, L. van Luxemburg and A. Gade, “Sound Strength Calibration Methods,” in Proceedings of 20th International Congress on Acoustics, ICA 2010 , Sydney, Australia, 2010.