7. INSTRUMENTATION FOR NOISE MEASUREMENTS

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NOISE CONTROLInstrumentation 7.17.INSTRUMENTATION FOR NOISE MEASUREMENTS7.1PURPOSES OF MEASUREMENTSThere are many reasons to make noise measurements. Noise data contains amplitude,frequency, time or phase information, which allows us to:1.2.3.4.5.6.Identify and locate dominant noise sourcesOptimize selection of noise control devices, methods, materialsEvaluate and compare noise control measuresDetermine compliance with noise criteria and regulationsQuantify the strength (power) of a sound sourceDetermine the acoustic qualities of a room and its suitability for various usesand many, many more .7.2 PERFORMANCE CHARACTERISTICSThe performance characteristics of sound measurement instruments are quantified by:Frequency Response - Range of frequencies over which an instrument reproduces thecorrect amplitudes of the variable being measured (within acceptable limits).Typical Limits over a specified frequency range:Microphones 2dBTape Recorders 1 or 3 dBLoudspeakers 5 dBDynamic Range - Amplitude ratio between the maximum input level and theinstrument’s internal “noise floor” (or self noise). All measurements should be at least 10dB greater than the noise floor. The typical dynamic range of meters is 60 dB, more isbetter.J.S. Lamancusa Penn State12/4/2000

NOISE CONTROLInstrumentation 7.2Response Time - The time interval required for an instrument to respond to a full scaleinput, (limited typically by output devices like meters, plotters)7.2SOUND LEVEL METERSThe primary tool for noise measurement is the SoundLevel Meter (SLM). The compromises with sound levelmeters are between accuracy, features and cost. Theprecision of a meter is quantified by its type (see standardsIEC 651-1979, or ANSI S1.4-1983 for more details)Type 0Type 1Type 2Type 3Laboratory reference standard, intended entirely for calibration of other soundlevel metersPrecision sound level meter, intended for laboratory use or for field use wherethe acoustical environment can be closely controlled. (ballpark estimate: 5000)General purpose, intended for general field use and for recording noise leveldata for later frequency analysis ( 500)Survey meter, intended for preliminary investigations such as thedetermination of whether noise environments are unduly bad. ( 50, RadioShack)Table 7.1 Principal allowable dB tolerance limits on sound level meters (refANSI S1.4-1983)CharacteristicType 0Type 1Type 2Accuracy at calibrationfrequency to referencesound levelAccuracy of completeinstrument for randomincidence soundMaximum variation oflevel when theincidence angle isvaried by 22.5 0.4 dB 0.7 dB 1.0 dB 0.7 1.0 1.5Maximum allowablevariation of sound levelfor all angles ofincidence 0.5 (31-2000 Hz) 1.5 (5000-6300 Hz) 3 (10000-12500 Hz) 1.0 (31-2000 Hz) 1.5 (5000-6300 Hz) 3 (10000-12500 Hz) 1.0 (31-2000 Hz) 2.5, -2 (5000-6300Hz) 4, -6.5 (10000-12500Hz) 1.5, -1(31-2000 Hz) 4 (5000-6300 Hz) 8, -11 (10000-12500Hz) 2.0 (31-2000 Hz) 3.5 (5000-6300 Hz)* (10000-12500 Hz) 3(31-2000 Hz) 5, -8 (5000-6300 Hz)* (10000-12500 Hz)* none specifiedThe most basic SLM will have an analog or digital output of A-weighted (or unweighted)sound pressure. Additional features can include octave or 1/3 octave filters, frequencyweighting networks (A,C, D, Lin), time averaging, and interface to a PC for data storageand plotting.J.S. Lamancusa Penn State12/4/2000

NOISE CONTROLInstrumentation 7.3Response Time: Sound level meters commonly have settings of:“Fast” 200 msec response time (or sometimes 125 msec)“Slow 1 sec response timeThe Slow setting will smooth out transients and provide a steady, average value. TheFast setting is useful if you are interested in the transient events.If a noise is an impulse (very short duration, fast rise and decay) such as an explosion, orimpact, neither of these settings will give an accurate reading. Impulsive soundsmeasured on a fast or slow setting may be up to 30 dB less than the true peak level. Moreexpensive meters also have a “Peak” response option. Peak measurements (of impulsivesounds) are made by storing the peak level (which might be reach in a few milliseconds)in a capacitor, then displaying the peak value of the meter.Weighting NetworksFrequency weighting networks (implemented with electronic filters) are built into soundlevel meters to provide a meter response that tries to approximate the way the earresponds to the loudness of pure tones. These weighting curves are directly derived fromthe Fletcher/Munson equal loudness contours. See section 4.2 for more information onweighting networksFigure 7.17.3Frequency characteristics of weighting networks commonly found insound level meters.MICROPHONESMicrophones are available from a variety of suppliers (B&K,GenRad, Aco, etc) in a wide range of sizes (1” to 1/8” diameter).Most microphones used for precision measurements are of theJ.S. Lamancusa Penn State12/4/2000

NOISE CONTROLInstrumentation 7.4condenser type. The construction of a condenser microphone is shown in Figure 7.2.Figure 7.2 Schematic and cutaway views of a typical condenser microphoneThe basic operating principle for a condenser microphone is: a thin diaphragm and thefixed back plate, separated by a thin air gap, form the two plates of a capacitor. Pressurefluctuations from incoming sound waves cause the diaphragm to vibrate, changing the airgap. This changes the capacitance, which is measured electronically and converted into avoltage by appropriate circuitry, usually contained in a separate unit called a preamplifier. Instrumentation grade microphones are specially designed to have negligiblesensitivity to temperature and humidity, and have excellent long term stability (see Table7.2).Table 7.2 Specifications of general purpose B&K condenser microphonesSizeModelFrequency response ( 2 dB)Sensitivity (mV/Pa)Temperature Coefficient (dB/ C)Expected Long Term Stability at20 .01 600years/dB½”41334-40KHz12.5-.002 1000years/dB1”41452.6-18KHz50-.002 1000years/dBMicrophone selection depends on two primary parameters: Sensitivity - ratio of microphone output voltage to input pressure amplitude (inunits of mV/Pa). In general, larger microphones have a greater sensitivity. Frequency Response - variation in sensitivity as a function of frequency (theideal is a perfectly flat response). Frequency response is specified as a range overwhich the output signal deviates less than 2 dB. Typical frequency responsecurves are shown in Figure 7.3. Smaller microphones have a wider frequencyresponse. At high frequencies (when wavelength approaches the diameter of themicrophone) diffraction effects occur which alter the frequency response. Theseeffects are dependent on the incidence angle of the sound waves (see Figure 7.4).J.S. Lamancusa Penn State12/4/2000

NOISE CONTROLInstrumentation 7.5The frequency response curve approaches flat for 90 degrees (grazing) incidence.Each microphone is supplied with calibration curves, which can be used tocompensate for this diffraction effect at high frequencies (but most people don’t).To minimize this error, use as small a microphone as possible.1”1/2”1/4"1/8”Figure 7.3 Frequency response of B&K condenser microphones of various sizes usingan electrostatic actuatorFigure 7.4 Directional characteristics of ½” condenser microphoneJ.S. Lamancusa Penn State12/4/2000

NOISE CONTROLInstrumentation 7.6Microphone typesPressure – designed to be used for coupler measurements, i.e. directly coupled to a testchamberRandom (diffuse field) – designed to give optimum frequency response for randomincidence sound (equal probability of sound from all directions, such as in a reverberantchamber)Free Field - designed to give optimum frequency response for sound from a particularincidence angle (usually 0 degrees)Figure 7.5Microphone orientationJ.S. Lamancusa Penn State12/4/2000

NOISE CONTROL7.5Instrumentation 7.7FREQUENCY ANALYSIS (1/n Octave)The most basic measurement any sound level meter can make is an overall dB level.This is a single number, which represents the sound energy over the entire frequencyrange of the meter. It provides no information about the frequency content of the sound.We can obtain information on the frequency content by using filters. The most commonare octave band and 1/3 octave band filters. The most frequency detail is provided byFFT analysis.Octave Band - Measures the total acoustical energy within the passband of a band passfilter. The term “octave” denotes a doubling in frequency. Hence, each octave bandcovers a frequency range of one octave. We refer to the octave band by its centerfrequency. The center frequencies of successive filters are separated by one octave. Thepreferred octave band center frequencies (by international standard) are: 31.5, 63, 125,250, 500, 1000, 2000, 4000, 8000 and 16000 Hz. The shape of a typical octave filter isshown in Figure 7.4 below. The bandwidth of a filter is the width in frequency betweenthe –3 dB points. This is an example of a constant percentage bandwidth filter. Thewidth of octave filters progressively increases with frequency. When plotted on a logscale, the shape of the band response is independent of frequency. The output of apercentage bandwidth filter is: dB/BandwidthFigure 7.4Characteristics of an octave band filterJ.S. Lamancusa Penn State12/4/2000

NOISE CONTROLInstrumentation 7.8An octave band filter is not a perfect bandpass filter (it is physically impossible to buildone). There is a finite “rolloff” or skirt on each side of the band. As can be seen inFigure 7.5, adjacent filters overlap each other slightly.Figure 7.5 Complete filter characteristics for a typical octave band filter set1/1 Octave Filter Relationships:f l 2 1 / 2 f cf u 21 / 2 f cf ci 1 2 f ci center frequencies of adjacent filtersf l lower cutoff frequency (to - 3 dB point), Hzf u upper cutoff frequency (to - 3 dB point), HzOne-third, one-tenth octave analysis - More detail is sometimes needed to obtainadequate frequency resolution, hence the need for bandwidths finer than one octave. Thechoice of filter bandwidth depends on the nature of the measured noise - is it broadbandor does it have significant pure tones which you want to identify? Closely spaced puretones will not be discovered by a wide bandwidth analysis.1/3 octave - Each full octave is spanned by three 1/3 octave bands1/3 Octave Filter Relationships:f l 2 1 / 6 f cf u 21 / 6 f cf ci 1 21/ 3 f ci 1.26 f ci center frequencies of adjacent filtersJ.S. Lamancusa Penn State12/4/2000

NOISE CONTROLInstrumentation 7.91/10 octave – Each full octave is spanned by ten 1/10 octave bands (not very commonanymore, due to the widespread availability of inexpensive FFT analyzers)General 1/n Octave Filter Relationships:f l 2 (1 / 2 n ) f cf u 2 (1 / 2 n ) f cf ci 1 2 1 / n f ciThe center frequencies and upper and lower limits of the octave and 1/3 octave filterbands are shown in Table 7.3 below.Table 7.3Center and cutoff frequencies (Hz) for standard full octave and1/3 octave filtersOctave1/3 OctaveLower limitCenter FreqUpper limitLower limitCenter FreqUpper limit11 Hz16 Hz22 Hz14.1 Hz16 Hz17.8 0113601600022720141301600017780177802000022390J.S. Lamancusa Penn State12/4/2000

NOISE CONTROLInstrumentation 7.107.6 FFT ANALYSISThe FFT Fast Fourier Transform, is a narrow band, constant bandwidth analysis (thefrequency resolution does not change over the frequency range)FFT refers to the numerical algorithm used to calculate the Fourier transform in “realtime” (in less time than it takes to acquire the actual data). In layperson’s terms, the FFTdetermines the frequency content of a time signal. The mathematical definition of aFourier transform is:X(f ) ò x(t )e j 2π ftdt The FFT algorithm discretizes this calculation. It requires a finite number of time datapoints, typically a power of 2, such as 512 (29) or 1024. It is a transformation from timeto frequency.TIME DOMAIN:x(i t) amplitudeat time intervals of t (seconds),N data samplesFREQUENCY DOMAIN:X(j f) amplitude(complex) at frequencyintervals of f (Hz),FFT f 1/(N t)N/2 valid pointsFigure 7.6 The Fast Fourier TransformSome sample time data (induction noise from a 2.5L 4 cylinder engine), and itsassociated frequency spectrum obtained by FFT are shown in Figure 7.7.a) time historyFigure 7.7b) frequency spectrumInduction noise data from a 4 cylinder engine running at 3000 RPM, wideopen throttleJ.S. Lamancusa Penn State12/4/2000

NOISE CONTROLInstrumentation 7.11Useful things you can do with a FFT Analyzer: multiple channel analysis (transfer functions)signal averaging (in time or frequency)modal analysis (determine mode shapes)display time signals (like a digital oscilloscope)order tracking (for rotatingequipment)correlation analysismathematical operations (* / -,integration, derivative)frequency zoomwaterfall plots (spectral maps)store data to disk for later analysisand plottingdata interface to MATLAB foradditional calculations and displayFigure 7.8Waterfall plot, showing variation invibration spectrum with timeThings to watch out for: bad data, faulty transducers, poor signal/noise ratiochoice of data window - use Hanning or Flat-top for steady, continuous data;Rectangular (sometimes called “Boxcar”) for transient or impact dataadequate signal levels ( 10 dB over ambient, no overloads)sufficient frequency range to see everything of interestsufficient frequency resolution (only accurate to f/2) – can be difficult toseparate closely spaced peaksJ.S. Lamancusa Penn State12/4/2000

NOISE CONTROL7.7Instrumentation 7.12COMBINATION OF TWO OR MORE FREQUENCY BANDSA typical task is to determine the octave band level from 1/3 octave band measurements,or to calculate an overall level from individual octave or 1/3 octave bands. This is justlike summing dB’s from several sources as in Section 6.1.The general expression for total pressure over the interval of interest is:nPT2 å P12 å P12 P22 .Pn2i 1æ P10 log 10 ç TçPè refand in dB’s:2n æö 10 log 10 å ç Pi çi 1 è Prefø2nö 10 log 10 å 10 LPi / 10 i 1øThe total power in an octave band is related to the individual 1/3 octave bands by:2Poctave P12 P22 P32 (because we are adding energy, which is proportional to P2)LP 10 log102L p2L p3LpPoctave 10 log10 é10 1 /10 10 /10 10 /10 ù dB2êëúûPrefExample 1:The levels in the 400, 500 and 630 Hz 1/3 octave bands measure 72, 74, 68 dB. What isthe octave band level for the 500 Hz band?10 log10 (10 7.2 10 7.4 10 6.8 ) 76dBExample 2: Calculate the overall level for the following octave band measurements:(Answer: 102.6 dB)Center Freq1252505001000200040008000dB798094100949488J.S. Lamancusa Penn State12/4/2000

NOISE CONTROL7.8Instrumentation 7.13CONVERSION FROM ONE BANDWIDTH TO ANOTHERThere may be cases where you acquire data with one width of filter, and you later findyou really needed to know the level over a different bandwidth. If you recorded all the1/3 octave bands, it’s easy to convert to full octaves, just logarithmically add the dB’s asshown in the last section. However, what if you only measured one 1/3 octave band, butyou desperately need to know the level over that entire octave? You have lost someinformation, but if you assume that the energy is uniformly distributed over the entireband (and there are no pure tones), then you can still make an estimate:Prms2Energy in band (output of filter with width f)is proportional to area under the curvefFigure 7.9 The output of a filter is determined by the amplitude and the bandwidthFirst, let us define:Spectrum level Sound level (dB) read by an ideal analyzer with a 1 Hz bandwidthWe can relate spectrum level to levels taken with other bandwidths by:P 2 PSL2 fwhere: P rms pressure output of filter with bandwidth fPSL rms pressure in 1 Hz bandThis implicitly assumes that the total energy in a given band is proportional to p2 timesthe width of the band (i.e. the area under the p2 curve). To convert a pressuremeasurement from one bandwidth to a different bandwidth:fwhere: P1 rms pressure output over bandwidth f1P22 P12 2f1P2 rms pressure output over bandwidth f2and in terms of sound pressure level:L2 L1 10 log10f2f1Example: the output of the 100 Hz 1/3 octave band is 58 dB, how much would bemeasured using the 125 Hz full octave band?J.S. Lamancusa Penn State12/4/2000

NOISE CONTROLInstrumentation 7.14Answer: assuming that the level is uniform over the entire octave band,L2 L1 10 log107.9f2f1 58 10 log 103 58 4.8 63 dB1MEASUREMENT OF PURE TONES WITH OCTAVE OR 1/3OCTAVE FILTERS:If we have a prominent pure tone in addition to background noise:Pure tonePressureBackground noisefFrequencyFigure 7.10 A pure tone combined with background noiseThe total power in the band is proportional to:2Pband å P 2 over the band22 Ppuretone background noise (Σ P )Examples:1. A pure tone of 80 dB at 120 Hz is combined with broadband noise which measures 75dB in the 125 Hz band. What is the total SPL in the 125 Hz band? (Answer: 81.2 81dB)2. A pure tone which measures 93 dB alone is combined with broadband noise whichmeasures 80 dB by itself. What is the combined noise level? (Answer: 93.2 93 dB)Important Result: A pure tone will measure the same dB level on any bandwidthanalysis, provided it is significantly higher (by at least 10 dB) than the background level.J.S. Lamancusa Penn State12/4/2000

NOISE CONTROLInstrumentation 7.157.10 SYNTHESIZING OCTAVE OR 1/3 OCTAVE BANDS FROMDISCRETE FFT DATAWe can use an FFT analyzer to measure and record a noise spectrum (the sound pressureamplitude at discrete, evenly spaced intervals of frequency, f). In some situations, itmight be convenient to not have to haul around an octave band sound level meter too, sois there a way that we can use the FFT data to construct or “synthesize” the octave banddata? The answer is a qualified “yes”.Each FFT data point represents the output of a filter which is f Hz wide. The overallenergy over a frequency band larger than f is proportional to the area under the Prms2curve:n2PBAND å Pi 2i 12where: Pi mean square acoustic pressure of the ith FFT data pointn number of FFT data points that fall within the bandwidth of the synthesizedfilter (see Table 7.2 for octave and 1/3 octave limits) f FFT frequency increment or “bin” size (Hz)dBBAND 10 logand in dB’s:nåP2ii 1Example: The noise from a portable circular saw is measured with a microphone and anFFT analyzer. For comparison purposes, the 1/3 octave sound pressure levels weresimultaneously measured using a Type I sound level meter. The FFT spectrum of themicrophone output from 0 – 5000 Hz is shown in Figure 11. Calculate the 1/3 octavelevel in the 100 - 200 Hz bands. The microphone output for a 250 Hz pistonphonecalibrator is –15.2 dBV. The FFT analysis particulars: N 800 points, Fs 12800 Hz, f 6.25 Hz, Hanning window.959085SPL 005000Frequency HzFigure 7.11 Noise spectrum for circular sawJ.S. Lamancusa Penn State12/4/2000

NOISE CONTROLInstrumentation 7.16Table 7.4 Partial FFT data for Circular SawFrequency (Hz)MicrophoneOutput- dBVCalibratedDB 2659.06212.50-67.8

INSTRUMENTATION FOR NOISE MEASUREMENTS 7.1 PURPOSES OF MEASUREMENTS There are many reasons to make noise measurements. Noise data contains amplitude, frequency, time or phase information, which allows us to: 1. Identify and locate dominant noise sources 2. Optimize selection of noise control devices, methods, materials

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