Engineering Noise Control - Theory and practice

Published simultaneously in the USA and Canada by Taylor & Francis 270 Madison Avenue, New York, NY 10016, USA. Despite rigorous efforts by all involved in the publication process, some typographical or editorial errors may occur, and readers are encouraged to bring them to our attention where they represent material errors.

PREFACE

The treatment of two-stage vibration isolation has been extended and non-dimensional plots provided to allow estimation of the effect of various parameters on isolation performance. Appendix A, which in the first edition contained example problems, has been replaced with a simple derivation of the wave equation.

ACKNOWLEDGMENTS

Fundamentals and Basic Terminology

INTRODUCTION

In the following text, the chapters are arranged to follow a natural progression, guiding the reader from the basic fundamentals of acoustics to advanced noise control methods. Successful use of noise control technology requires a basic understanding of the physical principles of acoustics and how they can be used to reduce excessive noise.

NOISE-CONT ROL STRATEGIES

Sound Source Modification
Control of the Transmission Path
Modification of the Receiver
Ex isting Facilities
Facilities in the Design Stage
Airborne versus Structureborne Nois e

Changing the power source to reduce the noise generated is often the best way to control noise. In new facilities and products, quantifying the noise problem at the design stage can range from easy to difficult.

Figure 1.1 Impact noise reduction: (a) variable height collector;

ACOUSTIC FIELD VARIABLES .1 Variables.1 Variables

The Acoustic Field
Magnitudes
Dispersion
Acoustic Potential Function

For gases, the speed of sound depends on the temperature of the gas through which the acoustic wave propagates. Flexural wave speed is dependent on the frequency of the disturbance and is therefore dispersive.

WAVE EQUATION

Plane and Spherical Waves
Plane Wave Propagation
Spherical Wave Propagation
Wave Summation
Plane Standing Waves
Spherical Standing Waves

See the discussion after equation (1.17) in section 1.4.2 for a definition of using the prime number N. For harmonic waves, the solution given by equation (1.41) can also be written in the following specific form.

Figure 1.2 Representation of a sound wave: (a) compressions and rarefactions of a sound wave in space at a fixed instance in time;

MEAN SQUARE QUANTITIES

Note that the largest difference between the maximum and minimum pressure occurs for a standing wave when p = 0 at the boundary. However, standing waves (with smaller differences between maximum and minimum pressure) will also occur for conditions where the pressure at the outer boundary is not equal to 0.

ENERGY DENSITY

If there is a chance of confusion, the averaging variable is added as a subscript; For example, the mean square sound pressure, averaged over time and space, can also be written as +p2(r, t),S,t. In this case, the following useful relationship between the amplitude and the root mean square value of a sinusoidally varying single frequency quantity is given by:

SOUND INTENSITY

Definitions
Plane Wave and Far Field Intensity
Spherical Wave Intensity

A general expression for the sound intensity I(r ), is the time average of the instantaneous intensity given by equation (1.64). Equation (1.71) gives the instantaneous intensity for the case considered here in the form of the pressure amplitude, p0, and the particle velocity amplitude, u 0.

SOUND POWER

The second term tends to zero as the distance r from the source to the observation point becomes large; that is, the second term is negligible in the far field of the source. Time integration of equation (1.78), taking into account that the integral of the second term is zero, gives the same expression for the intensity of a spherical wave as obtained earlier for a plane wave (see Equation (1.74)) .

UNITS

In this case, the source was treated as radiating uniformly in all directions. At sea level and 20 EC, the characteristic impedance is 414 kg m-2 s-1, so for plane and spherical waves, applying equation (1.87a) gives the following: a).

Figure 1.6 Sound pressure levels of some sources.

SPECTRA

Frequency Analysis

For example, if the piston moves erratically but cyclically so that it produces the waveform shown in Figure 1.8(c), the resulting sound field will consist of a combination of sinusoids of different frequencies. By minor adjustments to the calculated values recorded in the table, it has been possible to arrange the center frequencies of a third octave so that ten times their logarithms are the band numbers of column one on the left side of the table.

Figure 1.8 Spectral analysis illustrated. (a) Disturbance p varies sinusoidally with time t at a single frequency f 1 , as in (b)

COMBINING SOUND PRESSURES .1 Coherent and Incoherent Sounds.1 Coherent and Incoherent Sounds

Addition of Coherent Sound Pressures
Beating
Addition of Incoherent Sounds (L ogarithmic Addition)
Subtraction of Sound Pressure Levels
Combining Level Reductions

Some useful properties of adding sound levels will be illustrated with two further examples. The following example will show that the addition of two sounds can never result in a sound pressure level more than 3 dB greater than the loudest sound level.

IMPEDANCE

Initially, the sound pressure level at an observation point is due to linear propagation and reflection in the ground plane between the source and receiver. In situation A, before the change, the sound pressure level at the observation point is LpA and the propagation loss over the path reflected in the ground plane is 5 dB.

FLOW RESISTANCE

The flow resistance of unit thickness of material is defined as the flow resistance R1 which has the units Pa s m-2, often referred to as MKS rays per meter. The dependence of flow resistance on bulk density, ρm, and fiber diameter, d of the porous material should be noted.

The Human Ear

BRIEF DESCRIPTION OF THE EAR

Ex ternal Ear
Middle Ear
Inner Ear
Cochlear Duct or Partition
Hair Cells
Neural Encoding
Linear Array of Uncoupled Oscillators

The auditory nerve is connected to the central dividing wall through the nucleus of the cochlea. The efferent system is connected to the outer hair cells and to the afferent nerves of the inner hair cells (Spoendlin, 1975).

Figure 2.1 A representation of the pinna, middle and inner ear (right ear, face forward)

MECHANICAL PROPERTIES OF THE CENTRAL PARTITION

Basilar Membrane Travelling Wave
Energy Transport and Group Speed
Undamping
The Half Octave Shift
Critical Frequency Band
Frequency Resolution

At the threshold of audibility, the damping ratio will be minimal, on the order of 0.011. This consideration suggests that the critical band is associated with a segment of the central partition.

Figure 2.4 Typical half octave shift due to exposure to a loud 700 Hz tone.

NOISE INDUCED HEARING LOSS

A role for outer hair cells in explaining the distortions of received sound caused by the oral cavity is proposed. Clearly, if the outer hair cells cannot perform this function, the overall response of the ear will be limited to the narrow dynamic range of the inner hair cells.

SUBJ ECTIVE RESPONSE TO SOUND PRESSURE LEVEL

Mask ing
Loudness
Comparative Loudness and the Phon
Relative Loudness and the Sone
Pitch

The lines in the figure are arranged so that all variable sounds of the same number sound. In each case, the phone scale is chosen so that the number of phones is equal to the sound pressure level of the reference tone at 1 kHz.

Figure 2.7 Example of masked audible spectra where the masker is either a tone or a narrow band of noise

Instrumentation for Noise Measurement and Analysis

MICROPHONES

Condenser Microphone
Piezoelectric Microphone
Pressure Response
Microphone Sensitivity
Field Effects and Calibration
Microphone Accuracy

Referring to Equation (3.19) shows that the output voltage of a microphone is directly proportional to the area of the diaphragm. Essentially, both the phase and the amplitude of the sound pressure distribution across the diaphragm of the microphone are affected.

Figure 3.1 A schematic representation of a condenser microphone and equivalent electrical circuit.

WEIGHTING NETWORKS

However, when using a calibrator of this type, the frequency response of the microphone is assumed to be flat over the entire frequency range. Given the sound spectrum shown in line 1 of the table below, find the overall unweighted (linear) sound level in decibels and the A-weighted sound level in dB(A).

SOUND LEVEL METERS

Slightly better sound level meters have a sensitivity adjustment that allows it to be calibrated, and they show the A-weighted average sound level over a specified time. Top class sound level meters can display octave and 1/3 octave band spectra, as well as Leq, LAeq and statistical quantities such as L10 (sound pressure level exceeded 10% of the time) and L90.

CLASSES OF SOUND LEVEL METER

Some sound level meters have a third response called “impulse response” (with a default time constant of 35 milliseconds) for measuring impulsive sounds such as forges. Many sound level meters with an impulse response characteristic also have the option of measuring peak sound levels using a standard time constant of 50 µseconds.

SOUND LEVEL METER CALIBRATION

Electrical Calibration
Acoustic Calibration
Measurement Accuracy

During calibration, the sensitivity setting on the sound level meter is adjusted to read a value equal to the sound pressure level produced by the pistonphone calibrator. Large errors may indicate damage to the sound level meter or calibrator, and in such cases both should be returned to the manufacturer for inspection.

NOISE MEASUREMENTS USING SOUND LEVEL METERS

Microphone Mishandling
Sound Level Meter Amplifier Mishandling
Microphone and Sound Level Meter Response Characteristics
Background Noise
Wind Noise
Temperature
Humidity and Dust
Reflections from Nearby Surfaces

Whenever foam windshields are used, the microphone manufacturer's advice should be followed regarding the slight effect on microphone sensitivity at high frequencies. When not in use, store the equipment in a dry place and protect the microphone with a dessicator cap.

TIME-VARYING SOUND

Such potential effects can be expected when the dimensions of an object are comparable to or larger than the sound wavelength being measured. The likely effect on the sound field can be judged by referring to Table 5.1 and the accompanying discussion of Section 5.9.1 of Chapter 5.

NOISE LEVEL MEASUREMENT

Nearby objects that may affect the sound radiation from a source must often remain undisturbed for the purpose of the measurement; for example when assessing operator noise levels. At other times their presence may be highly undesirable, such as when assessing the true acoustic performance of a particular machine.

DATA LOGGERS

The type of noise measurement will also depend on the type of noise source; steady state and impulsive noises require different types of measurements.

PERSONAL SOUND EXPOSURE METER

Periodic Mass production, dB value, LAeq Sound level meter Octave or 1/3 octave varying surface grind or noise dose Integrate sound analysis if noise noise level meter is excessive. Hammer blow,L and "peak" value Impulse sound Difficult to assess.Aeq Single impulse material handling, level gauge or SLM Very harmful for punch press with "peak" hold hearing.

Table 3.2 Noise types and their measurement CharacteristicsType of sourceType of measurementType of instrumentRemarks Constant Pumps, electric Direct reading of A- Sound level meterOctave or 1/3 octave continuous noise motors, gearboxes, weighted v

RECORDING OF NOISE

When LAeq is used to determine the average sound level over an eight-hour period, it is defined as LAeq,8h. It is good practice to record at the start of a recording the following information: microphone position, unweighted sound pressure level measured with a sound level meter, calibration level, attenuator settings and a description of the test setup and weather conditions.

SPECTRUM ANALYSERS

Multi-channel analyzers (with two channels being the most common) offer the further capability of investigating interrelationships between different input signals. Sometimes these cards do not have anti-aliasing filters (see Appendix D) and great care is required in their use due to "folding back" (Randall, 1987) at lower frequencies of signals having a higher frequency than the digital sampling rate of the analyzer.

INTENSITY METERS

Sound Intensity by the p–u Method
Sound Intensity by the p–p Method
Frequency Decomposition of the Intensity

The phase difference is related to the velocity of the acoustic particles in the space between the two receivers and can be used to calculate an estimate of the particle velocity up to a frequency of 6 kHz. As before, I(ω) represents the real-time (or active) average intensity at frequency ω and Ir(ω) represents the amplitude of the reactive component.

ENERGY DENSITY SENSORS

Remember that the intensity results must be multiplied by the frequency resolution of the cross-spectral density to find the single-frequency intensity. Note, however, that most spectrum analyzers measure both the cross-spectrum and the cross-spectral density, and that the frequency multiplication has already been done in the cross-spectrum.

SOUND SOURCE LOCALISATION

Nearfield Acoustic Holography (NAH)
Helmholtz Equation Least Squares Method (HELS)
Beamforming
Direct Sound Intensity measurement

The measurements are then used to predict the complex acoustic pressure and particle velocity on a plane that approximates the surface of the source (prediction plane). It is also possible to obtain quantitative measurements of the sound power emitted by the source (Hald, 2005).

Figure 3.7 Circuit used to process signals from an energy density sensor to produce an r.m.s signal proportional to energy density as well as individual pressure and velocity signals (the latter being particularly useful for active noise control applicatio

Criteria

INTRODUCTION

Noise Measures

The "C-weighted" sound exposure level is determined by substituting the C-weighted noise level for the A-weighted level in equation (4.6). The next step is to calculate the tone-corrected perceived noise level (LPNT) for each time interval.

Figure 4.1 Sound exposure of a single event.

HEARING LOSS

Threshold Shift
Presbyacusis
Hearing Damage

Thus, it is clear that the level of sound pressure at the entrance of the ear can be very different from the level of the sound field that propagates freely in the absence of the audience. Loss caused by exposure to excessive noise usually occurs first in the frequency range from about 4000 Hz to 6000 Hz, which is the range of greatest sensitivity of the human ear.

Figure 4.2 Threshold shift due to presbyacusis: M = men; W = women. Speech sounds:

HEARING DAMAGE RISK

Requirements for Speech Recognition
Quantifying Hearing Damage Risk
International Standards Organisation Formulation
Alternative Formulations
Observed Hearing Loss
Some Alternative Interpretations

Here, Y is the age of the population and following the international standard ISO 1999 it is assumed that exposure to excessive noise starts at the age of 18 years. If the observation that hearing loss due to noise exposure is a function of the r.m.s pressure integral with time, then n = ½ and.

Table 4.1 Values of the coefficients u, v and L used to determine the NIPTS for the median value of the population, N 0,50

HEARING DAMAGE RISK CRITERIA

Continuous Noise
Impulse Noise
Impact Noise

The criterion in Figure 4.6 is arranged to be equivalent to a continuous exposure of 90 dB(A) over an eight-hour period, and this point is marked on the diagram. We enter this value on the abscissa of Figure 4.6 and draw a vertical line until it intersects the corresponding curve.

Figure 4.5 Idealised waveforms of impulse noises. Peak level = pressure difference AB; rise time = time difference AB; A duration = time difference AC; B duration = time difference AD (+ EF when a reflection is present).

IMPLEMENTING A HEARING CONSERVATION PROGRAM

SPEECH INTERFERENCE CRITERIA

Broadband Back ground Noise
Intense Tones

The figure also shows the volume that the interlocutor would automatically use (expected volume) as a result of the background noise level. If there are specular surfaces, the scale on the abscissa should be shifted to the right by 5 dB.

Figure 4.7 Rating noise with respect to speech interference.

PSYCHOLOGICAL EFFECTS OF NOISE

Noise as a Cause of Stress
Effect on Behaviour and Work Efficiency

Where the noise level fluctuates greatly, the scale on the abscissa may shift to the left by 5 dB. On the other hand, quiet conditions are not optimal for a simple task, and performance improves with the addition of noise.

AMBIENT NOISE LEVEL SPECIFICATION

Noise Weighting Curves
Speech Privacy

The RC number is the average of the sound level of the octave band 500 Hz, 1000 Hz and 2000 Hz, expressed to the nearest whole number. In order to determine whether the noise is "hissing", the NCB curve that best fits the sound levels of the octave band between 125 Hz and 500 Hz is determined.