View a demo of this course

The objective of this course is to provide an introductory overview of basic acoustics as related to a variety of applications. Course focuses on understanding the fundamental concepts and techniques of air-borne sound, as well as audio engineering and noise control engineering.

Topics include: 

• Acoustic Waves in Air and Solids
• Speech and Hearing
• Decibels dB; A- and C- Weighting Scales
• Frequency Analysis: Spectrum and Octave Band
• Sound Reflection, Transmission, and Refraction
• Directionality of Sources, Receivers, and Arrays
• Loadspeakers and Audio Systems
• Microphones and Sound Intensity Probes
• Sound Level Meters
• Sound in Rooms and Ducts
• Outdoor Sound Propagation
• Environmental Acoustics and Community Noise
• Acoustic Filters and Noise Mufflers
• Other topics of interest to course participants

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Learning Options:

• On-site tailored instruction: Three-day on-site class
• Web-based self-paced lessons: Video streaming
• On-line mentoring: To be selected

Also see Noise Control Engineering

• Web-based self-paced lessons: Flash movie with six topics

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Course Materials:

• Each student receives a copy of the instructor's course notes.
• Optional texbooks are available at an additional charge

View a demo of this course

The objective of this course is to provide an introductory overview of noise and vibration control with relevant applications. Course focuses on understanding the fundamental concepts and techniques of controlling sound waves in air and vibrations in systems and structures.

Topics include:

• Basic Sound and Vibration Concepts
• Source-Path-Receiver Model of Noise Control
• Sources of Tonal and Broadband Noise: 
   - System and Structure Considerations
   - Flow-noise and Flow-induced Responses
• Machinery Vibration and Control:
   - Damping, Isolation Mounts, Dynamic Absorbers
• Noise Control Treatments:
   - Barriers, Sound Absorption and Decoupling
• Basics of Active Control
• Examples of interest to course participants

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Learning Options:

• On-site tailored instruction: Three-day on-site class
• Web-based self-paced lessons: Flash movie, six topics
• On-line mentoring: To be selected

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Course Materials:

• Each student receives a copy of the instructor's course notes.
• Optional texbooks are available at an additional charge

The objective of this course is to provide an introductory overview of structural vibrations and sound interaction including related analytical analysis techniques.     

Topics include:

• Sound Waves in Air and Structures
• Propagating and Standing Waves in Structures:
   - Rods, Beams, Plates, Shells
• Reflection-transmission at Structural Discontinuities
• Sound-Structure Interaction: Coincident Effects
• Sound Radiation from Structures
• Frequency Response Functions:
   - Impedance, Mobility, Receptance, Inertance
• Reciprocity Applications to Structures
• Basics of Statistical Energy Analysis (SAE)
• Mean-Value Approach to Vibration Response
• Basic Modal Analysis of Structures
• Examples of interest to course participants

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Learning Options:

• On-site tailored instruction: Three-day on-site class
• Web-based self-paced lessons: Video streaming
• On-line mentoring: To be selected

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Course Materials:

• Each student receives a copy of the instructor's course notes.
• Optional texbooks are available at an additional charge

A series of two, three-day on-site courses intended for engineers and other technical personnel and managers who have a work-related need to understand basic underwater acoustics and sonar system concepts. This is an introductory course and participants need not have any prior knowledge of sound or vibration, underwater phenomena, or signal processing.  These courses  can serve as part of a new employees’ orientation. Emphasis is placed on illustrating phenomena and principles through appropriate applications, in-class demonstrations, and worked-out examples. Topics are presented with an emphasis on concepts, not on mathematics.

4A.  Underwater Acoustics I & Passive and Active Sonar (3-Days)

Introductory Concepts

• Historical background
• Sonar systems and platforms
• ASW analysis and strategies

Basic Sound and Vibration

• Sound in fluids and solids
• Waveforms and frequency analysis
• Sound energy, power, intensity, and pressure
• Decibel (dB) scales and references

Basic Underwater Acoustics 

• Sound speed profiles  (SSP)
• Cavitation considerations
• Ambient noise: frequency and directional characteristics
• Self-noise issues
• Propagation loss: spreading and absorption

Underwater Sound Propagation

• Sound reflection and refraction
• Ray acoustics and convergence zones (CZ)
• Sound channels: surface ducts, SOFAR, RAP
• Surface effects: scattering, Doppler, Lloyd mirror
• Bottom effects: scattering, refraction, lateral waves

Passive Sonar Systems

• Passive sonar equation and signal processing
• Radiated noise levels and explosive charges
• Octave and narrow band analysis
• Target detection threshold (DT)  and ROC curves
• Figure of merit and range assessments

4B.  Underwater Acoustics II & Select Sonar Systems (3-Days)

Active Sonar Systems

• Active sonar equation and signal processing
• Reverberation noise: Volume, surface, and bottom
• Active pings:  Pure tones (PTL and PTS) and FM
• Range – Doppler ambiguity
• Doppler effects on target returns
• Own Doppler nullification (ODN)

Shallow Water Acoustics

• Littoral environmental factors
• Ambient noise
• Multipath effects: signal stretch
• Shallow water waveguides: lossy normal modes
• Internal waves and currents

Sonar Transducers and Arrays

• Transducer elements: sensitivity and directionality
• Sonar arrays: linear, planar, cylindrical, and spherical
• Array processing: beamforming, steering, bearing angle
• Vector sensors and arrays

Target Characteristics

• Target construction: single and double hulls
• Target strength measurements
• Mono-static and multi-static target scattering
• Hull geometry and structure effects
• Echo formation and anechoic coatings

Selected Underwater Acoustics and Sonar Systems

• Autonomous Underwater Vehicles (AUV) and Remote Operated Vehicles
  (ROV)
• Expendable Bathythermograph (XBT), Sound Velocimeter (XSV) and their
  errors
• Other topics of interest to course participants

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Learning Options:

• On-site instruction can be tailored to present topics of host organization’s
  specific interest.
• On-line mentoring can be provided.

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Course Materials:

• Each student receives a copy of the instructor's course notes.
• Optional texbooks are available at an additional charge

The objective of this course is to provide a refresher of basic engineering mechanics concepts and principles. Course focuses on understanding how to set up, analyze and interpret the static and dynamic behavior of simple mechanical systems.

Topics include:

• Review of basic vectors and matrix mathematics
• Creating free-body diagrams with forces, moments and couples
• Resultants and equilibrium force systems on rigid bodies
• Forces in trusses, beams and structures
• Review of basics of stress-strain relationships
• Shear and moment diagrams, Mohr’s circle
• Centroid and moments of inertia of machines and structures
• Frictional Forces
• Kinematics and kinetics of particles and rigid bodies (linear and angular)
• Conservation of work and energy
• Conservation of impulse and momentum
• Introduction to simple mechanical vibrations
• Topics of interest to course participants

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Two Learning Options:

1. On-site tailored instruction: Two- to three-day on-site class

2. Web-based self-paced lessons with weekly on-line mentoring with instructor (see demo of this version of course)

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Course Materials:

• Each student receives a copy of the instructor’s course notes.
• Review textbook with worked-out examples.

Background Information

Jump to section:

• Calculus with Analytical Geometry
• Differential Equations with Laplace Transforms
• Partial Differential Equations & Boundry Value Problems
• Linear Algebra with Excel Applications
• Applied Statistics with Excel Examples
• Fourier Transforms with Engineering Applications

"Use It or Lose It"

Among engineers, the old saying “use it or lose it” aptly applies to the technical skills we learned in our undergraduate or graduate courses. An absence from the classroom of only a few years can significantly diminish our math and basic engineering skills.

Math as a Tool

 As an engineer with over 25 years of university experience teaching both undergraduates and graduates, I have found that students who lack a basic understanding of engineering fundamentals, and equally importantly, of how to use "math as a tool," often encounter difficulties, not only as they pursue their engineering education, but also when they try to handle more technically advanced work assignments.

Goal

As an educator and an engineer, my goal for all the math courses is to instill in participants a working knowledge of how math is used as a tool for problem solving, from initial identification of assumptions through final interpretation of results. By taking these courses in a convenient two-day format, participants can quickly get back up on the "learning curve," without spending weeks or months in often unproductive self-study or re-taking a formal undergraduate or graduate level math course.

Objective

The objective of these two-day refresher courses is to provide the opportunity for technical professionals to upgrade their basic engineering and math skills quickly and conveniently. The courses are intended for engineers and others who have a need or desire to enhance their technical ability and increase their professional competency. The courses have proven particularly helpful for those taking technical classes, pursuing either graduate or undergraduate studies, or desiring just a review or an introductory overview. Emphasis is placed on how to set up, analyze, and interpret engineering problems.  

Review and Overview

Courses designated as "Review" are directed toward participants who have had some exposure to the subject, as would be the case for the Calculus or the Differential Equations courses. Courses designated as "Introductory Overview" are directed toward participants who have had no previous experience with the subject but still have a need to learn more about the topic and to be introduced to the topic in as non-threatening a way as possible. This might be the case for the Statistics or the Partial Differential Equations courses.

Course Materials

Each participant receives a copy of the instructors course notes and an appropriate review text containing many examples and worked-out problems.

Some Work-Related Aspects of the Math Refresher Courses

1. Engineers, particularly those given new assignments, are often asked to review technical reports or professional journal articles to become familiar with a technical project.  Typically, this literature contains mathematical equations and derivations that the engineer needs to interpret in order to understand the relevance of the technical material presented.
2. Like foreign languages, one’s skill with mathematics can diminish without consistent use.  For sometimes years, many engineers are assigned tasks that do not require them to use the math skills they once had.  As a result, if their jobs require them to “think mathematically,” they need to get back up on the “knowledge curve.”  They could attempt to re-acquire these skill on their own, but that could take weeks and still not provide the competency and insight needed.   The goal of the math refresher short courses is to review and enhance these basics skills in the context of practical engineering examples and to accomplish that in a convenient two-day format.
3. There is a great deal of emphasis today on the use of computers to help design and develop systems and components.  However, much of what is being programmed is based on analytical analysis of fundamental laws and principles of engineering.  Examples of the old adage  “garbage in - garbage out” can easily occur if programmers do not have a good understanding of both the analytic methods and the physical laws they are asked to implement.
4. When required to take specific technical training courses, many engineers find themselves overwhelmed by “the math” and do not derive full benefit from these courses as a result.

Calculus with Analytical Geometry 

The objective of this course is to provide a review of calculus and analytical geometry. Emphasis is placed on how to use math as a tool  to set up and interpret engineering problems.

This course is intended for those with a work-related need, those taking technical training classes, pursuing either graduate or undergraduate studies, or desiring just a refresher.

Topics include:

• Analytica Geometry
• Differential Calculus
• Derivatives of Algebraic and Trigonometric Functions
• Extremes: Maximum & Minimum
• Related Rates Problems
• Integrals: Indefinite, Definite, and Numerical
• Integration Techniques: Substitution, by-parts, partial fractions
• Topics of interest to the course participants

• Engineering Applications Include:
  • Energy and Work
  • Lengths, Surface Areas, and Volumes
  • Moments of Intertia
  • Maximum and Minimum

Differential Equations with Laplace Transforms 

 The objective of this course is to provide a review of differential equations with Laplace transforms.  Emphasis is placed on how to use math as a tool  to set up and interpret engineering problems.

This course is intended for those with a work-related need, those taking technical training classes, pursuing either graduate or undergraduate studies, or desiring just a refresher.

Topics include:

• Linear First & Second Order Differential Equations
• Homogeneous and Non-Homogeneous Equations
• Initial and Boundary Value Problems
• Systems of Ordinary Linear Differential Equations
• Laplace Transforms with Method of Residue
• State Variables Formulation of Simple Systems
• Engineering Applications Include:
  • Electric Circuits,
  • Mechanical Vibrations,
  • Strength of Materials,
  • Control Systems,
  • Fluids Dynamics,
  • Heat Transfer

Partial Differential Equations & Boundary Value Problems 

The objective of this course is to provide an introductory overview of linear partial differential equations (PDE) as they apply in engineering. Basic physical laws are reviewed and applied to the derivation and interpretation of initial- and boundary-value problems.

This course is intended for those with a work-related need, those taking technical training classes, and those pursuing either graduate or undergraduate studies.

No previous experience with Partial Differential Equations is required.

Topics include:

• Review of Ordinary Differential Equations
• Boundary and Initial Value Problems
• Fourier Series and other Orthogonal Series
• Separation of Variables,
• Eigenfunction Expansions,
• Vector Analysis and Green’s Function,
• Differential Equations of Special Functions (Bessel, Legendra, etc.),
• Integral Transform Techniques: (Fourier, Bessel )
• Engineering Applications Include:
  • Structural Vibrations,
  • Modal Analysis,
  • Heat Transfer,
  • Fluids Dynamics,
  • Sound Waves,
  • Wave Guides

Topics of interest to the course participants.

Linear Algebra with Excel Applications 

The objective of this course is to provide a basic introductory overview of linear algebra and matrix analysis techniques used in engineering. Basic concepts are developed and explored through examples and geometrical interpretations.

This course is intended for those with a work-related need, those taking technical training classes, and those pursuing either graduate or undergraduate studies.

No previous experience with linear algebra nor matrices is required.

Topics include:

• Review of basic vector analysis and matrix algebra
• Systems of linear equations
• Square matrices and determines
• Inverse matrices techniques and features
• Orthogonal relations and inner product
• Diagonalization techniques
• Eeigenvalues and eigenvector problems
• Singular value decomposition (SVD)
• Principal component analysis (PCA) 
• Engineering applications including Excel examples from:
  • Engineering mechanics,
  • Mechanical vibrations,
  • Electric circuits,
  • Data analysis ,
  • Sensor calibration

Applied Statistics with Excel Examples 

The objective of this course is to provide a basic introductory overview of statistics and probability as they apply in engineering. Basic concepts are developed and explored through simple examples and graphical illustrations. The course also acquaints participants with numerical techniques of statistical analysis using Excel examples.

This course is intended for those with a work-related need, those taking technical training classes, and those pursuing either graduate or undergraduate studies.

No previous experience with probability or statistics is required.

Topics include:

• Frequency and Probability Distributions
• Means, Variances and Standard Deviations
• Combinational and Conditional Probabilities
• Discrete and Continuous Distribution Models: 
  e.g. Binomial, Normal, Triangular, Exponential, Weibull, et al
• Sampling Techniques and Sample Size Considerations
• Confidence Levels and Intervals
• Probability Plots and Percentiles
• Curve Fitting of Data; Goodness-of-Fit
• Linear Regression and Correlation Analysis
• Excel Examples of Statistical Analysis 
• Engineering Applications:
  • Manufacturing Tolerances,
  • System Reliability,
  • Structural Failure and Fatigue,
  • Signal Processing,
  • Design of Experiments

Topics of interest to the course participants. 

Fourier Transforms with Engineering Applications

The objective of this course is to provide an introductory overview of Fourier Transforms and their use in various engineering applications Basic concepts are developed and explored through simple analytical and graphical examples.

This course is intended for those with a work-related need, those taking technical training classes, and those pursuing either graduate or undergraduate studies.

No previous experience with Fourier analysis is required.

Topics include:

• Fourier Series of Period Functions:
  • Orthogonal functions and their selective analysis properties
  • Evaluation of discrete Fourier coefficients and phase
  • Time and spatial applications
• Fourier Transform of Non-Periodic Functions:
  • Convolution Theorem
  • Applications to frequency analysis
• Discrete Fourier Transforms:
  • Digital sampling considerations
  • Fast Fourier Transforms (FFT)
  • Window functions: Flattop, Hanning
  • Aliasing and leakage
• Engineering applications include:
  • Heat transfer,
  • Vibrational modes,
  • Signal processing,
  • Systems analysis

Topics of interest to the course participants. 

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Learning Options:

• On-site tailored instruction: Two-day on-site classes

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Course Materials: Each student receives:

• Each student receives a copy of the instructor's course notes.
• Review textbook with worked-out examples.

These refreshers are intended for engineers who want to renew their basic undergraduate math and engineering skills in a convenient self-paced manner. Fundamentals concepts are presented as web-based mini-movies that can be viewed at any time. In addition, relevant readings and example problems are assigned from a Fundamentals of Engineering Review Manual. Weekly internet-based discussions and problem Q&A sessions are conducted. Email correspondence between individual students and the instructor is encouraged.

Each of the following engineering refresher topics takes about five weeks to complete. Participants can enroll in one or more refresher.

Refresher — Engineering Mathematics (view a demo of this course)

Ten to twelve weekly topics :

• Math-1 — Introduction
• Math-2 — Units
• Math-3 — Conic Sections
• Math-4 — Trigonometry
• Math-5 — Linear Equations
• Math-6 — Roots of Equations
• Math-7 — Matricies
• Math-8 — Logarithms
• Math-9 — Vectors
• Math-10 — Complex Numbers
• Math-11 — Differential Calculus
• Math-12 — Derivatives: Special
• Math-13 — Integral Calculus
• Math-14 — Definite Integrals
• Math-15 — Differential Equations
• Math-16 — Engineering and Scientific Notation

<

Refresher — Engineering Mechanics (view a demo of this course)

Ten to twelve weekly topics:

• EMech 1 — Overview and Basic Rules of Mechanics
• EMech 2 — Force Systems
• EMech 3 — Systems in Equilibrium
• EMech 4 — Forces in Trusses and Frames
• EMech 5 — Pulley Systems
• EMech 6 — Friction Events
• EMech 7 — Centroid and Moments of Inertia
• EMech 8 — Kinematics and Kinetics
• EMech 9 — Conservation of Energy and Work
• EMech 10 — Conservation of Impulse and Momentum
• EMech 11 — Introduction to simple vibrations

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Learning Options:

• Web-based self-paced lessons including on-line mentoring 
• On-line mentoring session with the instructor.

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Course Materials:

• Participant receives one copy of the text Fundamentals of Engineering Review Manual by Michael R. Lindeburg, which contains brief review topics and many worked-out examples.

Summary:   
This three-day, on-site, course is intended to introduce engineers and other technical personnel to the fundamentals of making shock and vibration measurements and to the use of Matlab to analyze and interpret the measured vibratory data. Practical demonstrations are presented on the use of accelerometers and related data acquisition instrumentation. Emphasis is placed on a student being able to understand the basics of Matlab programing and the use of the Matlab  “Signal Processing Toolbox” and the Matlab “Data Acquisition Toolbox.”   Applications relevant to the class participants are demonstrated and discussed. (This course would also benefit those involved in sound measurement and analysis, as well as those interested in learning about Matlab and its Toolbox applications.)

Objective:
The goal of this course is for students to:

1. Understand the fundamental principles upon which vibration analysis is based.
2. Select and use accelerometers for shock and vibration measurement.
3. Learn to use a digital Data Acquisition system (DAQ) to record vibration signals.
4. Learn to use Matlab, including its Signal Processing and Data Acquisition Toolboxes, to:
   1. Perform basic mathematical calculations
   2. Perform filter and spectral analysis of recorded vibration signals
   3. Display and document analysis results
   4. Import raw measurement (signal) data and digitally store analysis results

Materials:
Each participant receives a copy of the instructor’s course notes, including a CD containing all Matlab examples and appropriate reference articles, as well as a copy of the textbook: Getting Started with MATLAB  by Radra Pratap.  

Schedule of Topics:

Day 1:  Fundamentals of Vibration

1. Introductory Concepts.   Review of signal types (periodic, random, etc.). Amplitude measurements.  Frequency and Fourier series (time and order based).  Types of frequency spectra (narrowband, PSD, CPBW). Measures of vibration (displacement, velocity, acceleration, and jerk).  Review decibels and complex numbers.
2.  Shock and Vibration Transducer.   Review of vibration sensors (accelerometers, laser vibrometers, etc.).  Accelerometer types and signal conditioning.  Accelerometer amplitude and frequency response.  Accelerometer mounting considerations.
3. Digital Signal Acquisition.   Digitization considerations.  Dynamic range resolution. Sampling frequency and aliasing.  Description and operation Data Acquisition systems (DAQ).

Day 2: Digital Signal Processing and Matlab Basics

3. Frequency Spectra. Sampling relationships: frequency range and resolution. Fourier Series and DFT/FFT (amplitude and phase considerations). Power spectra (PS) periodogram and power spectra density (PSD). Calculation of PS from Fourier Series and DFT. Windowing and leakage. The "picket fence effect." Averaging and errors in PS and PSD.
4. Time and Frequency Analysis: Time-domain functions. Time-frequency analysis. Frequency Response Functions (FRF). Digital filter characteristics (phase and time delays): Finite Impulse Response (FIR) and Infinite Impulse Response (IIR).
5. Matlab Basics. Overview of Matlab using interactive demonstrations and/or experiments. Matlab workspace and variables and calculation syntax. Basic graphics. Procedures for importing and storing data.

Day 3: Matlab Applications and Examples

6. Data Acquisition and Pre-Processing. Operating the DAQ and acquiring data using the Mathlab "Data Acquisition Toolbox." Importing and preparing data files for analysis using the Mathlab "Signal Processing Toolbox."
7. Vibration Analysis using Matlab. Filter analysis techniques and commands. Demos of vibration data using IIR and FIR filters. Matlab FDATOOL for filter design and analysis. Examples of Matlab spectral analysis techniques and commands including periodograms and spectrograms.
8. Selected Examples and Demonstrations. Matlab M-files will be provided to demonstrate the following: Stationary complex periodic and broadband (CPBW) autospectra; Transient ESD. Rotating machinery order analysis; Bandpass filtering analysis; Time integral and time-frequency analysis; Other Matlab applications based on discussions with the client.

Objective: 
Although most sounds that humans regard as audio begin and end as analog wave phenomena, modern processes for recording, manipulation, storage, transmission and reproduction of these sounds takes place increasingly in the digital domain.   This one-day on-site course provides an introduction to the basic principles and processes encompassed in digital audio systems.  The focus is on providing course participants with an understanding of digital technology as applied to fundamentally analog phenomena, primarily to enable or enhance human perception, as well the ability to “explain CD’s and MP3 players to your Great Aunt Gertrude.”

Approach: 
The course introduces fundamental concepts followed by a step-by-step explanation of the processes represented in a block diagram of a linear Pulse Code Modulation (PCM) audio recording and playback system. A brief introduction to perceptual coding is presented and  specific applications are discussed.  Demonstrations using PC-based real-time analysis software and recordings of digital audio artifacts and psychoacoustic phenomena are included.

Audience:
This course is intended as an introduction or review for EE’s, ME’s, CS/CSE grads and others who find themselves working on audio-related products or systems with the benefit of a course or two in DSP or vibrations, but without formal study of audio engineering or digital audio. The course is also suitable as an introductory overview for those who market, sell, distribute or install consumer, commercial¸ car audio or professional audio products and systems, as well as those whose work involves recording, storage, transmission or reproduction of audio signals using anything other than an analog tape recorder.    

Topics :

• Properties of audio signals; real time analysis
• Fundamental Processes
  • binary codes; discrete time sampling, aliasing; Quantization, quantization error, S/E vs. SNR; dither;  examples of errors and artifacts
• Digital Recording
  • modulation coding; Linear PCM;  anti-aliasing filters; sample & hold, jitter; analog-to-digital conversion, successive approximation; multiplexing, error correction, interleaving; channel codes
• Digital Reproduction
  • Linear PCM; digital-to-analog conversion; output sample & hold; output filters; oversampling; noise shaping; Compact Disc Digital Audio
• Psychoacoustics and Perceptual Coding
  • Hearing thresholds, loudness contours; critical bands and masking;  examples
  • data reduction coding; MP3 and AAC; proprietary formats; surround and HD formats

Instructor:
Dr. Chris Barber is the founder of Multipath Science and Engineering Solutions and has over twenty years’ experience in applied acoustic research ranging from acoustic testing of naval ships to characterization of professional audio systems.  He has taught courses and advised students in acoustics, audio and electrical engineering at the undergraduate, graduate and professional continuing education levels.

Resources:
Course participants receive a hard copy of the instructor’s course notes and selected reference materials.  Following the course, opportunities are provided to schedule a web-based follow-up Q&A session between the instructor and course participants. 

Objective:           
This short course provides an introduction to basic principles of sound and vibration measurements common across multiple disciplines.  The focus is on relating fundamental concepts used in the acoustic characterization of materials, machines and systems to actual physical measurements of these properties using real instrumentation and software applications under non-ideal test conditions.

Approach:           
Objectives, requirements and methods for obtaining high quality measurements of sound and vibration phenomena are presented and practical considerations are discussed.  Demonstrations of various measurements using common test instrumentation and examples of acoustic phenomena that impact measurements will be included throughout the day.  The course concludes with examples and discussion of real-world measurements tailored to course participant’s specific applications.  

Audience:           
This course is intended for engineers, system developers, technicians and others engaged in making measurements of sound, vibration or other dynamic signals.   The course is also suitable for those involved in interpreting, incorporating or marketing the results of such measurements.     

Topics:         

• Time and frequency domain properties of sound and vibration signals
• Measurement Instrumentation
  • sound level meters, oscilloscopes, frequency domain analyzers; 
  • analysis bandwidths, averaging;  spectrographs
• Measurement transducers
  • sensitivity, bandwidth, directivity, resonance;  calibration;
• Measurement Systems
  • signal conditioning, dynamic range, bandwidth; ADC parameters; data storage;
  • data analysis; special considerations for PC-based systems
• Measurements in noise
  • SNR optimization; RMS averaging;  energy and matched filter detection
  • cross-spectral methods; correlation techniques
• Selected measurement applications based on participant interest, including but not limited to:
  • Room acoustics (RT, ETC, STI); materials and structures  (α,NRC,TL, STC)
  • Audio and electro-acoustic system measurements
  • Environmental Noise Measurements (outdoor, industrial, marine)
  • Source localization; Underwater and ocean acoustic measurements
• Demonstrations using software apps and instrumentation provided by participants

Instructor:           
Dr. Chris Barber is the founder of Multipath Science and Engineering Solutions and has over twenty years’ experience in applied acoustic research ranging from acoustic testing of naval ships to characterization of professional audio systems.  He has taught courses and advised students in acoustics, audio and electrical engineering at the undergraduate, graduate and professional continuing education levels.

Resources:          
Course participants receive a hard copy of the instructor’s course notes and selected reference materials.  Following the course, opportunities are provided to schedule a web-based follow-up Q&A session between the instructor and course participants.  

Objective:           
Array theory is widely utilized in applications involving wave phenomena, from sonar and radar to radio telescopes and medical imaging.  More recently, array theory has been extended to audio applications with the widespread adoption of line array loudspeaker systems and ongoing interest in microphone arrays.  This one-day course provides an introduction to array theory and a basic understanding of the signal processing methods used with acoustic transducer arrays.    

Approach:           
The course begins with a brief review of mathematical concepts used in array theory, followed by a discussion of idealized sound sources and receivers and basic properties of acoustic transducers.   The theory of acoustic arrays as a collection of discrete transducers is developed and properties of arrays are explored.  Array signal processing concepts such as beamforming and spatial filtering are derived and explained.  Example arrays are considered and optimization of array parameters for specific applications is demonstrated using PC-based simulations.   A brief introduction to more advanced topics may be included subject to participant interest. 

Audience:           
This course is intended as an introduction to Array Theory for engineers, programmers and others working on projects or systems involving acoustic transducer arrays.  Some familiarity or prior exposure to mathematical concepts used in array theory is assumed but not required.    

Topics :         

• Introduction and Review
  • Complex exponential representation of acoustic waves; Fourier transforms
• Characterization of Acoustic Transducers
  • monopole radiation; ideal (simple) sources and receivers; distributed sources
  • source level; axial response; directional response and beam patterns; directivity, directivity index; 
• The Discrete Element Line Array
  • derivation of axial and directional acoustic fields; beam steering; array gain
  • array parameterization – aperture and element spacing, beam patterns and frequency response;
• Array Signal Processing
  • Array shading; time domain beamforming; frequency (phase) domain beamforming; source angle estimation, source localization; energy detection; matched filter processing
  • Beam patterns and spatial filtering; spatial Fourier transform
• Example arrays and applications
  • Wavenumber-to-size (ka) wavenumber-to-spacing (kd) and nearfield vs far field (kr) dependence
  • Array optimization ; array performance in realistic noise environments
  • Optional topics – adaptive beamforming; matched field processing; self-noise mitigation, other TBD

Instructor:           
Dr. Chris Barber is the founder of Multipath Science and Engineering Solutions and has over twenty years’ experience in applied acoustic research ranging from acoustic testing of naval ships to characterization of professional audio systems.  He has taught courses and advised students in acoustics, audio and electrical engineering at the undergraduate, graduate and professional continuing education levels.

Resources:          
Course participants receive a hard copy of the instructor’s course notes and selected reference materials.  Following the course, opportunities are provided to schedule a web-based follow-up Q&A session between the instructor and course participants.  

Objective:           
This one-day on-site course provides an overview of the subject of underwater radiated noise of ships and marine structures, including common sources of marine noise, noise reduction strategies , testing methods and analysis of results.

Approach:           
Noise sources, radiation characteristics and underwater propagation are introduced at the conceptual level and supported with simple calculations.  Common noise control approaches for new design or refit are presented and methods for making underwater noise measurements are explored in detail, with discussions of challenges and lessons learned.  The course concludes with examples of data analysis applications, including diagnostic investigation of noise problems, development of quiet ship operating guidance and demonstration of compliance with requirements and regulations.

Audience:           
This course is appropriate for engineers working in the design, construction or operation of ships, industrial facilities or offshore platforms, as well as for those responsible for conducting underwater noise measurements.  Naval architects, project and program managers, environmental compliance officers and others responsible for overseeing efforts where underwater radiated noise is of concern will also benefit.

Topics :        

• Introduction to underwater sound propagation
• Ship and industrial noise sources
  • propeller broadband noise, cavitation; rotating machinery; fluid-coupled systems; active acoustic emissions;  pile driving, construction; industrial operations; offshore platforms
• Noise reduction
  • propeller design; low-noise machinery; isolation mounts; path control;  operational strategies to reduce noise emission
• Radiated noise measurement approaches
  • acoustic test ranges; vessel-deployed systems; buoys and remote sensors; shallow water and pier-side measurements; navigation and range safety
• Radiated noise measurement system and test requirements
  • Hydrophones, cabling and signal conditioning; digital acquisition systems; real time monitoring; position tracking and ranging; ANSI / ISO standards
• Data analysis and applications of radiated noise measurements
  • spectral analysis; broadband levels; correlation and cross-spectral analysis; source and path investigations; environmental impact studies; ICES and IMO guidelines

Instructor:           
Dr. Chris Barber is the founder of Multipath Science and Engineering Solutions and has over twenty years’ experience in applied acoustics research, including radiated and shipboard noise testing of naval and research vessels.  He has taught courses and advised students in acoustics, audio and electrical engineering at the undergraduate, graduate and professional continuing education levels.

Resources:          
Course participants receive a hard copy of the instructor’s course notes and selected reference materials.  Following the course, opportunities are provided to schedule a web-based follow-up Q&A session between the instructor and course participants.