Course Notes for OSU ME 5241 Engineering Acoustics

171 Pages·2017·10.11 MB·English

by  Ryan L Harne

RL Harne ME 5241, Eng. Acoust. 2018 The Ohio State University

Course Notes for OSU ME 5241
Engineering Acoustics
Prof. Ryan L. Harne*
Department of Mechanical and Aerospace Engineering, The Ohio State University, Columbus, OH 43210, USA
*Email: [email protected]
Last modified: 2018-09-13 15:33

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RL Harne ME 5241, Eng. Acoust. 2018 The Ohio State University

Table of contents
1 Course introduction 6
1.1 Scope of acoustics and answers to "why should we study acoustics?" 6
1.2 Fundamental sound wave propagation phenomena 8
1.3 Waves and sounds 8
1.4 Wave propagation phenomena 9
1.4.1 Wavefronts 9
1.4.2 Interference 9
1.4.3 Reflection 10
1.4.4 Scattering 10
1.4.5 Diffraction 11
1.4.6 Refraction 12
1.4.7 Doppler effect 13
1.5 Further resources for an acoustics introduction 14
2 Introduction to human hearing and influences of noise 15
2.1 Outer ear 15
2.2 Middle ear 15
2.3 Inner ear 17
2.4 Noise and its influence on hearing 18
2.4.1 Influences of ultrasound on human hearing 19
3 Mathematics background survey and review 20
3.1 Mathematical notation 20
3.2 The harmonic oscillator 20
3.3 Initial conditions 21
3.4 Energy of vibration 22
3.5 Complex exponential method of solution to ODEs 23
3.6 Damped oscillations 27
3.7 Harmonically forced oscillations 29
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RL Harne ME 5241, Eng. Acoust. 2018 The Ohio State University

3.8 Mechanical power 33
3.9 Transfer functions 34
3.10 Linear combinations of simple harmonic oscillations 35
3.11 Further Examples 39
4 Wave equation, propagation, and metrics 41
4.1 One-dimensional wave equation 41
4.1.1 General solution to the one-dimensional wave equation 43
4.2 Harmonic waves 45
4.2.1 Harmonic waves in the complex representation 47
4.3 One-dimensional acoustic wave equation 48
4.3.1 Consolidating the components to derive the one-dimensional acoustic wave equation 52
4.4 Harmonic, plane acoustic waves 55
4.5 Acoustic intensity 57
4.6 Harmonic, spherical acoustic waves 58
4.6.1 Spherical wave acoustic intensity and acoustic power 60
4.7 Comparison between plane and spherical waves 61
4.8 Decibels and sound levels 62
4.8.1 Combining sound pressure levels 65
5 Elementary acoustic sources and sound propagation characteristics 66
5.1 Monopole and point acoustic sources 66
5.2 Sound fields generated by combinations of point sources 69
5.2.1 Directional wave propagation in geometric and acoustic far field acoustic wave radiation72
5.3 Source characteristics 76
5.4 Dipole acoustic sources 76
5.5 Reflection: method of images 78
5.6 Sound power evaluation and measurement 84
5.7 Outdoor sound propagation 89
5.7.1 Attenuation by the atmosphere 89
5.7.2 Attenuation by barriers 90
5.7.3 Total sound attenuation outdoors 90
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RL Harne ME 5241, Eng. Acoust. 2018 The Ohio State University

6 Acoustics instrumentation, measurement, and evaluation 92
6.1 Microphones 92
6.1.1 Characteristics of microphones 94
6.1.2 Selecting a microphone for the measurement 100
6.2 Sound level meters 101
6.3 Frequency bands 102
6.3.1 Using octave and one-third octave bands in acoustic measurements 103
6.4 Weighting networks 104
6.5 Locations to accurately measure sounds 108
7 Acoustics in and between rooms 111
7.1 The transient sound field in a room 111
7.2 Absorption of acoustic energy in a room 114
7.2.1 Diffuse field sound pressure level 117
7.2.2 Dissipation by fluid losses 118
7.3 Contribution of acoustic energy from the direct and reverberant acoustic fields 119
7.4 Sound transmission through partitions 120
7.4.1 Practical material compositions for sound absorption and blocking 125
7.5 Sound transmission through flexible partitions, panels 126
7.5.1 Influence of mass on transmission loss 129
7.5.2 Coincidence 129
7.6 Sound transmission class, STC 132
7.6.1 Methods to enhance STC 134
7.7 Impact insulation class, IIC 135
7.7.1 Methods to enhance IIC 136
7.8 Flanking 137
8 Applications of acoustics: noise control and psychoacoustics 140
8.1 Engineering noise control 140
8.1.1 Source-path-receiver methodology to engineering noise control 140
8.1.2 Noise exposure 141
8.1.3 Development for and enforcement of noise control criteria 142
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RL Harne ME 5241, Eng. Acoust. 2018 The Ohio State University

8.1.4 Vehicle noise 143
8.1.5 Speech interference 145
8.1.6 Noise criterion for rooms 147
8.1.7 Community reaction to noise 150
8.1.8 NIHL and occupational noise 151
8.1.9 Source-path-receiver methodology for noise control engineering 153
8.2 Psychoacoustics 154
8.2.1 Binaural hearing 154
8.2.2 Masking 163
8.2.3 The cocktail party effect 164

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RL Harne ME 5241, Eng. Acoust. 2018 The Ohio State University

1 Course introduction
Acoustics is "a science [dealing with] the generation, transmission, and reception of energy as vibrational
waves in matter" [1]. Thus, waves may propagate through gas, liquids, and solids. In this course, we give
attention to waves that propagate through gases and liquids (collectively termed fluids). These waves are
often termed sounds.
Sounds are pressure changes in a fluid medium transmitted from a source, through the medium, to a receiver.
Many sounds result from the vibrations of structures or materials. A few exceptions may be identified, such
as those sounds resulting from implosions, like cavitation, or explosions, like the ignition of combustibles.
In general, for an introductory treatment of acoustics such as will be undertaken in this course only a few
mathematical preliminaries, likely encountered before in a dynamics-related course, are required before
embarking on one's first study in acoustics. We will complete this review in Sec. 3.
1.1 Scope of acoustics and answers to "why should we study acoustics?"
Lindsay's wheel of acoustics is shown in Figure 1. It features the scope of acoustics circa 1964. This scope
and relation among the technical areas is still relevant today. The outer, four fields (Arts, Engineering, Earth
Sciences, Life Sciences) are related to technical subject areas (outer ring) and technical disciplines (inner
ring), which all share underlying physics and fundamental principles (core). The distinction from 1964 to
today is that one may identify new technical disciplines for the inner ring, such as those that are multi-
disciplinary due to emergent trends and fabrication capabilities. Representative additional technical
disciplines may include thermo- and aeroacoustics such as those encountered in various vehicle systems
contexts on land and in air [2] [3], and may include subjects pertaining to microscale acoustics associated
with microfluidics and micro-manipulation practices [4] [5].
The Acoustical Society of America (ASA) has largely emulated the structure of Lindsay's wheel towards
the formation of the Technical Committees that help facilitate society activities and engagements,
http://asa.aip.org/committees.html. In this course, we focus on how these fields of Engineering, the Arts,
Earth Sciences, and Life Sciences utilize acoustical principles. Greater emphasis will be placed on problems
pertaining to Engineering although many of our topics are multi-disciplinary at the core. Our studies will
include subjects of hearing, noise, room acoustics, electroacoustics, sonic and ultrasonic engineering, and
psychoacoustics. To exemplify the importance for these diverse contexts of acoustics, a few examples are
worthwhile.
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RL Harne ME 5241, Eng. Acoust. 2018 The Ohio State University

Figure 1. Lindsay's wheel of acoustics, adapted from R. B. Lindsay, J. Acoust. Soc. Am. 36, 2242 (1964).
Example: Effectively engineering the acoustic qualities of rooms is essential to promote effective speech
intelligibility [6]. In rooms with too little acoustically absorptive surfaces, the reverberation time of speech
will result in adverse reflections for the listener, making it challenging to understand the message. This
phenomenon is exacerbated in the presence of background noise. This course will describe the design and
implementation methods needed to correctly tailor the acoustic qualities of rooms, such as classrooms,
auditoriums, office spaces, concert halls, household spaces, and so forth, in the ways that promote speech
intelligibility and other relevant ergonomic factors.
Example: Humans have binaural hearing, meaning that two ears are used to hear which gives rise to an
ability to more effectively locate sources of sound. Interaural-time and -level differences, ITD and ILD,
respectively, are the principal factors that govern the ability to locate sound sources [7]. The field of
electroacoustics takes advantage of these factors to create virtual sound fields using a minimal number of
acoustic transducers, such as "surround sound" audio playback in movies. This course will describe the
fundamental principles that result in "steered" sound, which is a basis for acoustic signal processing
methods used in advanced electroacoustic systems. This course will also introduce the concepts of human
binaural hearing and the intriguing nuances that found our hearing sense.
A wealth of other examples of applications is available at http://acousticalsociety.org/education_outreach
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1.2 Fundamental sound wave propagation phenomena
Before diving in, it is valuable to learn about the basic phenomena of sound wave propagation at a high
level [8]. We will return to certain of these concepts in detail and in mathematical ways later in the course.
1.3 Waves and sounds
Waves in fluids result from the oscillation of fluid particles due to pressure differences on either sides of
the particles. In a significant proportion of applications, these particle oscillations are so insignificantly
small with respect to the length of the acoustic wave (wavelength) that we classify these oscillations as
linear. Thus, linearized analyses of the sound wave propagation are justified. Consequently, studies of many
wave propagation phenomena are greatly eased.
Many sound waves originate from interaction with vibration structural surfaces. The pressure differences
in the fluid may result from the vibration of a structural surface that pushes against the adjacent fluid. For
instance, one can imagine a machine being turned on that "makes noise". The surfaces of the machine that
interface with the fluid are moving, which gives rise to fluid-structure interactions at the surface. The fluid
particles adjacent to the surface will oscillate at the same frequency as the frequency of the machine surface
vibration, according to a continuity of fluid-structure displacement at the interface. Consequently, pressure
differences are created in the fluid adjacent to the machine that radiate away from the machine as acoustic
waves. This fundamental wave behavior is illustrated in Figure 2.

Figure 2. Sound waves created from vibrating surfaces. The colored fluid particles are the same from one time to the next.
The study of vibrations is distinguished from waves by the example shown in Figure 2. Namely, vibrations
are associated with the oscillation or general dynamics of a body, for instance the structural surface of the
machine or an individual fluid particle. On the other hand, waves are associated with both the oscillations
of the body and the resulting spatial transmission of energy in the form of a wave. In Figure 2, the colored
fluid particles are the same from t to t . These particles, like the neighbors, merely oscillate back and
1 2
forth. Yet, due to phase relationships of the oscillations, a wave is generated that transmits energy
(sometimes termed information) through space.
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RL Harne ME 5241, Eng. Acoust. 2018 The Ohio State University

These are distinct phenomena that do not have counterparts in a study only of vibrations. Vibrations of a
body may be described by oscillations in time, whereas wave propagation involves oscillations of many
bodies through space and time.
1.4 Wave propagation phenomena
1.4.1 Wavefronts
When waves propagate, a wavefront is generated. The wavefront denotes a location of constant phase of
the wave that moves through the fluid. Oftentimes the wavefront is considered as a local maxima of the
wave.
In an open field or volume of fluid, a sudden point source of acoustic pressure will generate a travelling
wavefront that diminishes in amplitude in time due to spherical wave spreading, Figure 3 at left.
For a continuously generated, single frequency wave, a wavelength is identified. This is analogous to the
time length from peak-to-peak of a sinusoidal oscillation signal, but now one considers the spatial length
from peak-to-peak of the wave to define the wavelength. These features are shown at middle and right in
Figure 3.

Figure 3. Propagating wavefronts.
1.4.2 Interference
When wavefronts are created from multiple locations in a volume of fluid, the wavefronts interact when
arriving at the same place at the same time. Depending on the phases that occur at the locations of wave
interaction, different types of interference phenomena will be observed.
Constructive interference occurs when the peaks of the waves combine at the same location.
Destructive interference occurs when the trough from one wave combines with the peak of another wave.
Examples of constructive and destructive interference are shown in https://youtu.be/fjaPGkOX-wo, Figure
4. Two sources of waves are present in the fluid. The total wavefronts generated after a long time has
elapsed are shown. The locations shaded with lightest green or darkest black are where constructive
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RL Harne ME 5241, Eng. Acoust. 2018 The Ohio State University

interference has occurred. The locations of mid-green shading are where destructive interference has
occurred to effectively blur and greatly diminish the observation of waves.

Figure 4. Snapshot of time series from video https://youtu.be/fjaPGkOX-wo.
1.4.3 Reflection
When a wavefront arrives at a discontinuity in the fluid medium, a portion of the wave is reflected and a
portion of the wave is transmitted. When the discontinuity is a rigid boundary (also termed barrier) all of
the wave energy is reflected. One example of a nearly-rigid boundary is a concrete wall adjacent to an air
volume. Such near-total reflection is shown in the video https://youtu.be/8LrrWvfyqLo around time 3:25.
When the discontinuity is a soft boundary adjacent to a wavefront originally in air, such as sound in air
arriving at a grassy plain surface, the reflected wavefront does not have the same magnitude as the incident
wavefront due to partial transmission of the wave into the adjacent media. In the example of air and a grassy
plain, the adjacent media is the soil which acts a lot like a quasi-fluid due to the granular composition of
soil.
Reflected waves have a phase that depends on the difference in composition from the incident fluid medium
to the second fluid medium of wave impingement. When the second fluid medium is "harder" than the
incident fluid medium, the reflected wave will be in phase with the incident wave. When the second fluid
medium is "softer", the reflected wave will be out of phase.
1.4.4 Scattering
Wave reflections create effective new sources of waves at the reflection interface. For spherical waves
impinging upon a number of fluid discontinuities, the large number of reflections are collectively termed
the scattered waves. Examples of scattering may include reflections of road noise from a sequence of fence
posts or underwater sonar impinging on a school of fish. The total wavefield will be complex due to the
combinations of reflections and the directly radiated sound from source to receiver. Occasionally, sounds
combine with frequency-selective characteristics such that an original incident sound will be spectrally
filtered once the reflection is heard with the directly radiated waves.
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