In many texts, the reader will find "noise" described as "unwanted sound." This is a rather loose description, as that which is wanted by some may be unwanted by others. A 250 cc Yamaha V4 racing two-stroke, producing 72 unsilenced horse- power at 14000 rpm, and wailing its way up the Mountain in the Isle of Man TT race of 1967, produced a noise which was music to the ears of a thousand racing
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motorcycle fans. A nearby farmer, the owner of a thousand chickens vainly trying to lay eggs, viewed the same noise from an alternate standpoint. This simple example illustrates the quite subjective nature of noise assessment. Nevertheless, between the limits of the threshold of human hearing and the threshold of damage to the human ear, it is possible to physically measure the pressure level caused by sound and to assign an experimental number to that value. This number will not detail whether the sound is "wanted" or "unwanted." As already pointed out, to some it will be described as noise.
8.1.1 Transmission of sound
As initially discussed in Sect. 2.1, sound propagates in three dimensions from a source through the air or a gas as the medium of transmission. The fundamental theory for this propagation is to be found in Sect. 2.1.2. The speed of that propagation is given by A, where:
A=V(g*R*T)=V(g*P/D) (8.1.1) The value for the ratio of specific heats, g, is 1.4 for air and 1.35 for exhaust gas
when it is at a temperature around 35CPC. The value of the gas constant, R, is 287 J/kgK for air and 291 J/kgK for exhaust gas emanating from a stoichiometric combustion. Treating exhaust gas as air in calculations for sound wave attenuation in silencers produces little error of real significance. For example, at 400SC:
A ir=V(1.4*287*673)=520 m/s A*h=V(1.35*291*673)=514 m/s
As exhaust gas in a two-stroke engine contains a significant proportion of air which is short-circuited during the scavenge process, this reduces the already negligible error even further.
8.1.2 Intensity and loudness of sound
The propagation of pressure waves is already covered thoroughly in Sect. 2.1, so it is not necessary to repeat it here. However, the propagation of these small pressure waves in air, following one after the other, varying in both spacing and amplitude, gives rise to the human perception of the pitch and of the amplitude of the sound.
The frequency of the pressure pulsations produces the pitch and their amplitude denotes the loudness. The human ear can detect frequencies ranging from 20 Hz to 20 kHz, although the older one becomes that spectrum shortens to a maximum of about 12 kHz. For another introductory view of this topic, the reader should consult the books by Annand and Roe(1.8) and by Taylor(8.11)
More particularly, the intensity, E, is used to denote the physical energy of a sound, and loudness, Lp, is the subjective human perception of that intensity. The relationship between intensity and loudness is fixed for sounds which have a pure tone, or pitch, i.e., the sound is composed of sinusoidal pressure waves of a given frequency. For real sounds that relationship is more complex. The intensity of the
Chapter 8 - Reduction of Noise Emission from Two-Stroke Engines sound, being an energy value, is denoted by units of W/m2. Noise meters, being basically pressure transducers, record the "effective sound pressure level," which is the root-mean-square of the pressure fluctuation about the mean pressure caused by the sound pressure waves. This rms pressure fluctuation is denoted by dP, and in a medium where the density is D and the speed of sound is A, the intensity is related to the square of the rms sound pressure level by:
E=dP2/(D*A) (8.1.2)
The pressure rise, dP, can be visually observed in Plates 2.1-2.3 as it propagates away from the end of an exhaust pipe.
The level of intensity which can be recorded by the human ear is considerable, ranging from 1 pW/m2 to 1 W/m2. The human eardrum, our personal pressure transducer, will oscillate from an imperceptible level at the minimum intensity level up to about 0.01 mm at the highest level when a sensation of pain is produced by the nervous system as a warning of impending damage. To simplify this wide variation in physical sensation, a logarithmic scale is used to denote loudness, and the scale is in the units called a Bel, the symbol for which is B. Even this unit is too large for general use, so it is divided into ten sub-divisions called decibels, the nomenclature for which is dB. The loudness of a sound is denoted by comparing its intensity level on this logarithmic scale to the "threshold of hearing," which is at an intensity, E0, of 1 pW/m2 or a rms pressure fluctuation, dPO, of 0.00002 Pa, or 0.0002 ^bar. Thus, intensity level of a sound, ELI, where the actual intensity is E l , is given by:
ELl=log]0(El/E0) B
= 10*log](1(El/E0) dB (8.1.3)
In a corresponding fashion, a sound pressure level, Lpl, where the actual rms pressure fluctuation is dPl, is given by:
Lpl=log,0(El/E0) B
=10*log10(El/E0) dB
=10*log]()[(dPl/dP0)2] dB
=20*log10(dPl/dP0) dB (8.1.4)
8.1.3 Loudness when there are several sources of sound
Let the reader imagine he is exposed to two sources of sound of intensities E1 and E2. These two sources would separately produce sound pressure levels of Lpl and Lp2, in dB units. Consequently, from Eq. 8.1.4:
El=E0*antilog10(Lpl/10) E2=E0*antilog1(1(Lp2/10)
The absolute intensity experienced by the reader from both sources simultane- ously is E3, where:
E3=E1+E2
Hence, the total sound pressure level experienced from both sources is Lp3 where:
Lp3=10*logIO(E3/EO)
= 10*log|0{antilog]0(Lpl/10)+antilog10(Lp2/10)} (8.1.5) Consider two simple cases:
(a) The reader is exposed to two equal sources of sound which are at 100 dB.
(b) The reader is exposed to two sources of sound, one at 90 dB and the other at
100 dB. ' First, consider case (a), using Eq. 8.1.5:
Lp3=10*log10{antilog,0(Lpl/10)+antilogl0(Lp2/10)}
=10*log10{antilog 10(100/10)+antilog.n(100/10)}
=103.01 dB
Second, consider case (b):
Lp3=10*log|0{antilog10(Lpl/10)+antilogi0(Lp2/10)}
=10*log10{antilog (100/10)+antilogin(90/10)l
= 100.41 dB
In case (a), it is clear that the addition of two sound sources, each equal to 100 dB, produces an overall sound pressure level of 103.01 dB, a rise of just 3.01 dB due to a logarithmic scale being used to attempt to simulate the response characteristics of the human ear. To physically support this mathematical contention, the reader will recall that the noise of an entire brass band does not appear to be so much in excess of one trumpet at full throttle.
In case (b), the addition of the second weaker source at 90 dB to the noisier one at 100 dB produces a negligible increase in loudness level, just 0.41 dB above the larger source. The addition of one more trumpet to the aforementioned brass band does not raise significantly the level of perception of total noise for the listener.
There is a fundamental message to the designer of engine silencers within these simple examples: if an engine has several different sources of noise, the loudest will swamp all others in the overall sound pressure level. The identification and muffling of that major noise source becomes the first priority on the part of the engineer Expanded discussion on these topics are to be found in the books by Harris(8 12) and Beranek(8.13) and in this chapter.
Chapter 8 - Reduction of Noise Emission from Two-Stroke Engines 8.1.4 Measurement of noise and the noise-frequency spectrum
An instrument for the measurement of noise, referred to as a noisemeter, is basically a microphone connected to an amplifier so that the system is calibrated to read in the units of dB. Usually the device is internally programmed to read either the total sound pressure level which is known as the linear value, i.e., dBlin, or on an A-weighted or B-weighted scale to represent the response of the human ear to loudness as a function of frequency. The A-weighted scale is more common and the units are recorded appropriately as dBA. To put some numbers on this weighting effect, the A-weighted scale reduces the recorded sound below the dBlin level by 30 dB at 50 Hz, 19 dB at 100 Hz, 3dB at 500 Hz, 0 at 1000 Hz, then increases it by about 1 dB between 2 and 4kHz, before tailing off to reduce it by 10 dB at 20 kHz.
The implications behind this weighting effect are that high frequencies between 1000 and 4000 Hz are very irritating to the human ear, to such an extent that a noise recording 100 dBlin at around 100 Hz only sounds as loud as 81 dB at 1000 Hz, hence it is recorded as 81 dBA. To quote another example, the same overall sound pressure level at 3000 Hz appears to be as loud as 101 dB at 1000 Hz, and is noted as 101 dBA.
Equally common is for the noisemeter to be capable of a frequency analysis, i.e., to record the noise spectra over discrete bands of frequency. Usually these are carried out over one-octave bands or, more finely, over one-third octave bands. A typical one-octave filter set on a noisemeter would have switchable filters to record the noise about 31.25 Hz, 62.5 Hz, 125 Hz, 250 Hz, 500 Hz, 1000 Hz, 2000 Hz, 4000 Hz, 8000 Hz and 16000 Hz. A one-third octave filter set carries out this function in narrower steps of frequency change. The latest advances in electronics and computer-assisted data capture allow this process of frequency analysis to be carried out in e^en finer detail.
The ability of a measurement system to record the noise-frequency spectrum is very important for the researcher who is attempting to silence, say, the exhaust system of a particular engine. Just as described in Sect. 8.1.3 regarding the addition of noise levels from several sources, the noisiest frequency band in the measured spectrum is that band which must be silenced first and foremost as it is contributing in the major part to the overall sound pressure level. The identification of the frequency band of that major noise component will be shown later as the first step towards its eradication as a noise source.
The measurement of noise is a tedious experimental technique in that a set procedure is not just desirable, but essential. Seemingly innocent parameters, such as the height of the microphone from the ground during a test, or the reflectivity of the surface of the ground in the vicinity of the testing, e.g., grass or tarmac, can have a major influence on the numerical value of the dB recorded from the identical engine or machine. This has given rise to a plethora of apparently unrelated test procedures, such as those in the SAE Standards(8.16). In actual fact, the logic behind their formulation is quite impeccable and any reader embarking on a silencer design and development exercise will be wise to study them thoroughly and implement them during experimentation.
The Basic Design of Two-Stroke Engines 8.2 Noise sources in a simple two-stroke engine