Particle Motion – the flip side of
sound
1 Background
Galway-Mayo Institute of Technology (GMIT), Ireland, have partnered with Irwin Carr Consulting
(ICC), Northern Ireland (UK), to further our understanding of important aspects of our underwater
environment. This project is focussed on the real-world application of the research and the
impact it will have on our understanding of underwater sound propagation. With the technical
expertise of our industrial partner ICC, we will be able to offer facilities, technical knowledge,
sound sparring and guidance to an outstanding aspiring PhD student to carry out internationally
important work. This cross-border cooperation with both academia and industry involved is a
change to explore this field of science in a professional environment as well as an academic one.
The successful applicant will be employed by ICC during the project, while remaining associated
with GMIT, and receiving guidance from both organisations.
2 Introduction
For a long time we have characterised sound either in terms of how the local pressure oscillates
or how much energy passes through a given area per unit time. These two approaches lead to the
units we assign to sound to characterise it: Sound Pressure Level (dBSPL re 1 µPa) and Sound
Intensity Level (dBI re 1pW/m2).
Sound must propagate through matter. And as matter is made up of particles, those particles move
for the sound to travel. The movements are almost always oscillations around a mean position that
particles will return to after being affected by a sound. Those movement are called particle motion,
and can be measured and described with respect to the peak particle acceleration, velocity and
displacement, all ways to characterise the level of the associated sound.
Humans are, for the most part, sensing sound as pressure fluctuations between the two sides of
the tympanic membrane. This works because air is compressible. Seawater however, is almost
incompressible, with a bulk modulus of 2.34 GPa. This is 16,500-23,000 times1 the resistance to
compression of air. A liquid-filled middle ear would therefore not be able to detect fluctuations in
pressure, as it would lead to very minimal compression of the liquid-filled middle ear, with an
associated minimal displacement to detect for the inner ear (or other functional equivalent).
The high resistance to compression is what makes sound travel much faster in water than in air.
Bulk Modulus [Pa] – K
Density [kg/m3] – ρ
Sound speed [m/s] – c
1
Air (at sea level)
Seawater
142,000 2,340,000,000
1.225
1,029
340.5
1508.0
𝐾
Sound speed 𝑐 = √ 𝜌
Depending on whether the process is adiabatic.
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Marine mammals have air-filled ears, capable of detecting pressure analogously to us, but many
fish and most invertebrates have no air-spaces associated with their ear, rendering them
insensitive to pressure fluctuations.
In a large proportion of situations sound waves can be legitimately characterised as plane
compression waves moving though a fluid. In these situations, it’s straightforward to calculate the
particle motion elements:
For a plane wave in far field2:
𝑢=
𝑃
𝑎 = 𝑢 ∙ 2𝜋𝑓
𝜌∙𝑐
𝑥=
𝑢
2𝜋𝑓
(1)
With 𝑢 being particle velocity (m/s), 𝑃 pressure (Pa), 𝜌 water density (kg/m3), 𝑐 sound speed
(m/s), 𝑎 particle acceleration (m/s2), 𝑓 frequency (Hz) and 𝑥 particle displacement (m).
To assess whether the plane wave criteria is fulfilled the following equations can be employed:
𝑓𝑙𝑖𝑚.𝑠ℎ𝑎𝑙𝑙𝑜𝑤 =
𝑐𝑤
4𝐷√1−(𝑐𝑤 /𝑐𝑏 )2
(2)
𝑓𝑙𝑖𝑚.𝑝𝑙𝑎𝑛𝑒𝑤𝑎𝑣𝑒 =
𝜌
𝜋− 𝑏
𝜌𝑤
𝑐
2𝜋sin(cos−1 𝑤 )
𝑐𝑏
𝑐
∙ ( 𝑤) (3)
𝐷
With 𝑐𝑤 being the sound speed in water (m/s), 𝑐𝑏 sound speed in sediment (m/s), 𝐷 depth at
source, 𝜌𝑏 density of sediment, 𝜌𝑤 density of water.
The frequency given by 𝑓𝑙𝑖𝑚.𝑠ℎ𝑎𝑙𝑙𝑜𝑤 is the lowest frequency that will not propagate directly into the
sediment and 𝑓𝑙𝑖𝑚.𝑝𝑙𝑎𝑛𝑒𝑤𝑎𝑣𝑒 is the lowest frequency that will propagate as a plane wave under
the given circumstances3. These two equations yield very similar results given similar input. This
means that for a site with a depth of ten meters the pressure component of sounds with a
frequency under ~90 Hz will not propagate simply in the water column, and particle motion
cannot be inferred from pressure measurements (as obtained with a piezoelectric hydrophone).
Figure 1. Relationship between sound pressure level, frequency and peak particle motion in an example scenario.
2
3
>2 wavelengths from source
Higher frequencies will behave “normally”.
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3 Scope of PhD
3.1 MAPPING PARTICLE MOTION
It’s envisioned that the graduate take on the task of measuring pressure and peak particle
motion in a semi-controlled environment, such as a harbour enclosure or a dock. This should
result in a detailed characterisation of a real sound field.
3.2 MODELLING PARTICLE MOTION
The graduate will attempt to model the particle motion using a choice of modelling approach and
the available literature. The aim is to develop a tool that can approximate the particle motion
from source information such as source level and spectral distribution while incorporating
environmental factors.
3.3 THIRD SCOPE TO BE DESCRIBED BY APPLICANT.
Ideas include:
-
boundary layer investigation
non-compressional waves (Rayleigh or sheer waves)
4 Method of Application
Applications must include the following information (See page 5):
-
Personal Details
Academic Qualifications, Transcripts and Results
Demonstration of Proficiency in the English Language
Personal statement detailing the candidate’s experience and ambition
A project proposal, based on the ideas outlined in this document (Max 5 Pages)
5 Funding Notes
The main method of funding will be from the Irish Research Council (details) to which we will
apply for funding, upon receipt of your application. Under this scheme the graduate will be
employed by the industrial partner (ICC) on company terms.
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6 References
1. Particle motion: the missing link in underwater acoustic ecology. Nedelec, Sophie L., et al. 7,
Suffolk : Methods in Ecology and Evolution, 2016. doi: 10.1111/2041-210X.12544.
2. Jensen, F.B., et al. Computational Ocean Acoustics. 2nd. s.l. : Springer, 2011.
3. Propagation of underwater sound. Ainslie, M. Berlin : Springer, 2010, Principles of Sonar
Performance Modelling, pp. 439-512.
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PhD Application Form
Completed applications and supporting documents should be emailed to
[email protected]
The closing date for receipt of applications is 12:00 (GMT), Tuesday 31st January 2017
1 Candidate information
Full name: _____________________________________________________________________________ Title: _______
Address:
Street: _________________________________________________________ Number: ____________
Town: _________________________________ County/State: ________________________________
Post code: _____________________________ Phone:
E-mail: ____________________________
Female ꙱
Male ꙱
____________________________________
Citizenship: __________________________
2 Academic Qualifications
Current Study:
(if any)
______________ _________________
Degree
Major subjects
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Expected completion & result
__________
Institution
Completed studies: _____________
(Include transcript) Degree
_________________
Major subjects
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Completion & result
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Institution
Completed studies: _____________
(Include transcript) Degree
_________________
Major subjects
_____________________________
Completion & result
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Institution
3
Proficiency in the English Language
꙱ English is my first language.
Where English is not your first language acceptable recent proofs (<3 years old) include:
[Attach relevant document(s)]
-
An official document from a higher education institute proving >2 years of higher education fully in English
TOEFL Certificate; minimum score 570 (Paper) / 87 (Internet)
IELTS Certificate; minimum score 6.5
First Certificate in English of the University of Cambridge
Certificate of a University Language centre testifying mastery of the necessary knowledge of English to
function academically (i.e.: specifying CEF-level – C1)
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4
Personal Statement
Experience:
2 Page limit
Detail relevant projects, dissertations, essays or other experience.
Detail the particular skills that have prepared you for this programme.
Describe other capabilities that illustrate your capability, motivation and interests.
Ambition: Describe why you are particularly suited to pursue a higher degree by research;
Include a project proposal, based on the ideas outlined in the call document;
Describe your career aspirations after completing the postgraduate degree;
Explain how the programme will assist your achievement of these goals.
5
Disclaimer and Signatures
Candidate:
I certify that my answers are true and complete to the best of my knowledge.
If this application leads to an award of Scholarship, I understand that false or misleading information in my application
or interview may result in denial or termination of the award.
I understand that the Scholarship’s General conditions operate in conjunction with GMIT’s Academic Codes of Practice
and Conduct (http://www.gmit.ie/about/academic-policies). I confirm that I have read and understood these
documents.
Candidates signature: ________________________________________
Date: __________________
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