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LJUD I BYGGNAD OCH
SAMHÄLLEDELPHINE BARD
DIVISION OF ENGINEERING ACOUSTICS, LUND UNIVERSITY
D. Bard / VTAF01 / 19 Jan. 2016
Outline
Course Information
Introduction to Acoustics
Administration
Summary
Wave propagation
D. Bard / VTAF01 / 19 Jan. 2016
Teachers
• Lectures:
‒ Delphine Bard, KC-building (3rd floor)
• Exercises:
‒ Juan Negreira
• Laboratory:
‒ Juan Negreira
‒ Marie-Laure Divoux
• Administration:
– Christina Glans, KC-building (3rd floor)
D. Bard / VTAF01 / 19 Jan. 2016
Course material
• Handed out material
– Lecture notes : Grundläggande akustik
(E. Nilsson m.fl. avd för Teknisk Akustik 2008)
Finns att köpa på KFS
– Exercise material
– Laboration instructions
– Project task
– Formulae
• Website (course material will be uploaded here):
http://www.akustik.lth.se/utbildning/kurser/
D. Bard /VTAF05 / 19 Jan. 2016
Laboratories & Project taskLaboratories
• Tider bokas in på lista på föreläsningen (läsvecka 3-6)
1. Mätning av svängningar och vibrationer i balk och sträng
2. Mätteknik, ljudabsorption och ljudisolering
• Utförs i akustiklab i V-huset!
• Utförs i grupper om 2 studenter (ev 3)
– Förberedelseuppgifter
– Laborationsrapport
Projektuppgift – mätning och modellering
• Två fördefinierade uppgifter:
– Trafikbullersituation
– Rumsakustik, akustisk reglering
Alternativ: fri uppgift – lösa egendefinierat problem
• Genomförs i grupper om 2 studenter (ev 3)
Redovisas i skriftlig rapport som lämnas in Ons 2/3
Examination
• Tentamen (50 %)
– Måndag 14/3 kl 8.00-13.00 i Victoriastadion 2C.
– Blandning av teori och räkneuppgifter
– Hjälpmedel: Miniräknare och utdelat formelblad
• Projektuppgift (50 %)
– Betygsätts u, 3, 4, 5
– Komplettering i efterhand endast upp till betyg 3.
• Genomförda laborationer med godkända rapporter
Schema
• 28 h föreläsningar,
• 28 h övningar,
• 4 h laborationer
• Självstudier
Kursmål
• Kursen syftar till att ge studenterna grundläggande
kunskaper om ljud och dess effekt på människan
med tillämpning på bullerproblem som uppstår i
byggnad och samhälle.
Kursinnehåll
• Grundläggande akustiska begrepp 1v
• Fysisk och matematisk genomgång av akustik och
vågutbredning 2v
• Trafikbuller 1v
• Rumsakustik 1.5v
• Ljudisolering 1.5v
D. Bard / VTAF01 / 19 Jan. 2016
Outline
Course Information
Introduction to Acoustics
Administration
Summary
Wave propagation
Lindseys akustiska hjul
D. Bard / VTAF01 / 19 Jan. 2016
Why address sound issues?
• Noise affects people physiologically and psychologically
• At least 25 % of EU citizens are
exposed to noise in such extent that it
affects health and quality of life
• …
• Today, approximately 2 million people in
Sweden are exposed to a noise level
that exceeds the regulations set up by
the Swedish parliament
D. Bard / VTAF01 / 19 Jan. 2016
What is acoustics?• Acoustics: part of physics studying generation, transmission reception,
absorption, reproduction and control of sound
‒ Environmental ac., building ac., room ac., psychoac., musical ac…
• Sound: ondulatory movement produced in an elastic medium by a
vibratory source producing variations in the atmospheric pressure
‒ Characteristics: pitch, quality and loudness
‒ Noise: random (unwanted) sound
» Classified by ”colours”
Violet noise: +6 dB/octave
Blue noise: +3 dB/octave
White noise: flat power spectrum
Pink noise: -3 dB/octave
Brown noise: -6 dB/octave
D. Bard / VTAF01 / 19 Jan. 2016
Time & frequency domains (I)
Harmonic signal: y t = A sin ωt = A cos ωt + ∅ = A sin 2πf ∙ t
‒ Amplitude:
‒ Period [s]:
‒ Frequency [Hz]:
‒ Wavelength [m]:
‒ Propagation Speed [m/s]:
NOTE:
‒ Effective value (RMS):
FFT
T λ
A
c ≠ v
ARMS = A =1
∆t
t0
t0+∆t
y2 t dt , Aharmonicsignal
= A2
‒ Frequency domain
A
T = 1 f
f = 1 T
λ=cT= c f
c=f λ
D. Bard / VTAF01 / 19 Jan. 2016
Time & frequency domains (II)
• A more complex time signal (traffic load)
• Narrow band analyses
‒ Impractical, time-consuming
‒ Octave & 1/3 octave bands
FFT
NOTE: Spectrum (any magnitude plotted against frequency)
D. Bard / VTAF01 / 19 Jan. 2016
Octave and 1/3 octave bands
If fn is the cut-off lower frequency
and fn+1 the upper one, the ratio of
the band limits is given by:
where k=1 for full octave and k=1/3
for one-third octave band
fn+1
fn= 2k
D. Bard / VTAF01 / 19 Jan. 2016
The decibel (dB) & SPL
• Logarithmic way of describing a ratio
‒ Ratio: velocity, voltage, acceleration…
‒ Need of a reference
• Sound pressure level (SPL / Lp)
‒ p measured with microphones
‒ Frequency response of human hearing changes with amplitude
Lp = 10 log p2
pref2 = 20 log
p
pref
p = p f = RMS pressurepref = 2·10
−5 Pa = 20 μPapatm = 101 300 Paptot(t) = patm ± p(t)
D. Bard / VTAF01 / 19 Jan. 2016
Sound (acoustic) intensity
• Sound power per unit area [W/m2]
‒ Vector quantity: energy flow and direction
– In a free field:
• Types of propagation
‒ Plane:
‒ Cylindrical:
‒ Spherical:
• In decibels…
I = pv =1
∆t
0
T
p t v t dt
I = p2
ρc; I ∝ p2
I r ∝1
r2;
I ≡ constant ;
LI = 10 logI
I0; I0 = 1 pW
m2= 10−12 W m2
I(r) =∏
4πr2
I(r) ∝1
r
D. Bard / VTAF01 / 19 Jan. 2016
Sound (acoustic) intensity – example
• Ex: In a rock concert, measurements are performed next to you
yielding a value of 90 dB. Which level will a person who is 5
times further away from the speakers perceive, assuming…
‒ … plave wave propagation?
‒ … cylindrical wave propagation?
‒ … spherical wave propagation?
D. Bard / VTAF01 / 19 Jan. 2016
Frequency weightings (I)
• Correlate objective sound measurements with subjective human response
‒ A-weighting [dB(A)/dBA]: designed to reflect the response of how the
human ear perceives noise, i.e. 20 Hz-20 kHz
Only really accurate for relatively quiet sounds and pure tones?
Low frequency noise is suppressed (wind turbine noise?)
‒ C-weighting [dB(C)/dBC]: developed for high level aircraft noise
‒ Z-weighting: zero frequency weighting (un-weighted values)
‒ B-weighting: covers the mid-range between the A- and C-weighting
‒ D-weighting: designed for use when measuring high level aircraft noise
________________________________*Filters are defined in the standard IEC 61672
Fallen into disuse
D. Bard / VTAF01 / 19 Jan. 2016
Frequency weightings (II)
• Filters and calculation
Lweighted = 10 log 10(Ln+weighting)
10
D. Bard / VTAF01 / 19 Jan. 2016
Summation of noise (I)
• Types of sources
‒ Correlated (or coherent)
Constant phase difference, same frequency
Interferences (constructive/destructive)
‒ Uncorrelated (or uncoherent)
The total RMS pressure:
Lp,tot = 20 log
n=1
N
10Lp,n20
Lp,tot = 10 log
n=1
N
10Lp,n10
For uncorrelated sources, the 3rd term vanishes
ptot2 = p1
2 + p22+2
∆𝑡
t0
t0+∆t
p1 t p2 t dt
D. Bard / VTAF01 / 19 Jan. 2016
Summation of noise (II)
• Graphical methods
‒ Adding equally loud incoherent sources
‒ Adding two different sources
e.g. L1=61 dB / L2=55 dB
‒ Substracting two different sources
e.g. LS+N=65 dB / LN=60 dB
Lt= 62 dB
Lt= 63.4 dB
D. Bard / VTAF01 / 19 Jan. 2016
Single event noise metrics
• Maximum sound level (Lmax):
‒ Accounts only for sound amplitude [dB/dBA…]
• Sound exposure level (SEL) & Single event noise exposure level (SENEL)
‒ Total “noisiness” of an event. It takes duration into account
‒ If SENEL is measured for the period when the level is within 10 dB of the
Lmax, it will be essentially the same as SEL
D. Bard / VTAF01 / 19 Jan. 2016
Cumulative exposure metrics
• Equivalent SPL during the measurement time T (units: dB, dBA…)
Ex: Calculate the Leq,8h that corresponds to 105 dBA for 15 min.
Leq,T = 10 log1
T 0
Tp2(t)
pref2 dt =10 log
1
T 0
T
10Lp(t)
10 dt
D. Bard / VTAF01 / 19 Jan. 2016
Other indicators / Measurement of SPL
• Day and night average sound level (DNL or Lden)
• Community noise equivalent level (CNEL)
• Time above threshold
• Effective perceived noise level (EPNL)
• …
• Measurement of SPL: Sound level meter
‒ Microphone measures acoustic levels omni-directionally
‒ Sampling: Fast (0.125 s), Slow (1 s), Peak (impulse value 35 ms)
‒ Weighting filters (A, C…) built-in
‒ Calculation of Leq,T, building acoustic indicators, traffic noise…
‒ Calibrated
D. Bard / VTAF01 / 19 Jan. 2016
Outline
Course Information
Introduction to Acoustics
Administration
Summary
Wave propagation
D. Bard / VTAF01 / 19 Jan. 2016
Types of waves – classifications
• Depending on propagation media
‒ Mechanical waves (solids and fluids)
‒ Electromagnetical waves (vacuum)
• Propagation direction
– 1D, 2D and 3D
• Based on periodicity
– Periodics and non-periodics
• Based on particles’ movement in relation with propagation direction:
‒ Longitudinal waves (solids and fluids)
‒ Transverse waves (solids)
• … NOTE: waves do not transport mass, just energy
D. Bard / VTAF01 / 19 Jan. 2016
Types of waves in solid media
• Longitudinal waves (∞ medium ≈ beams)
– Quasi-longitudunal waves (finite ≈ plates)
• Shear waves
• Bending waves (dispersive)
cL =E
ρ
cqL =𝐸′
ρ=
E
ρ(1 − υ2)
csh =G
ρ=
E
2(1 + υ)ρ
cB = ω4 𝐵
𝑚B𝜕4vy
𝜕x4+m
𝜕2vy
𝜕t2= 0
G𝜕2vy
𝜕x2− ρ𝜕2vy
𝜕t2= 0
E′𝜕2vx𝜕x2
− ρ𝜕2vx𝜕t2
= 0
x
y
Plate: E, G, ρ, υ, h
m = ρh
Bplate =Eh3
12(1 − υ2)NOTE: torsional waves (beams and columns) are not address here
Bbeam = Ebh3
12
D. Bard / VTAF01 / 19 Jan. 2016
Waves in fluid media (I)
• Sound waves: longitudinal waves
‒ Pressure as field variable
‒ Velocity as field variable
Comparing both equations: (acoustic impedance)
𝜕2p
𝜕x2−1
c2𝜕2p
𝜕t2= 0
cair =γP0
ρ(T = 0°C)1 +
T
2 ∙ 273= 331.4 1 +
T
2 ∙ 273,cmedium =
D
ρ,
p x, t = p± cos(ωt ± kx) = p±e−i(ωt±kx)
𝜕2v
𝜕t2= c2
𝜕2v
𝜕x2v x, t =
1
ρc p± e
−i(ωt±kx)
Z ≡p±v±= ±ρc
k =2π
λ
D. Bard / VTAF01 / 19 Jan. 2016
Waves in fluid media (II)
Time and position dependency: p x, t = p+ cos ωt − kx = p+e−i(ωt−kx)
D. Bard / VTAF01 / 19 Jan. 2016
Other types…
• In reality, combinations of aforementioned waves can exist, e.g.
• Surface waves
Water waves
(long+transverse waves)
Particles in clockwise circles. The radius
of the circles decreases increasing depth
Pure shear waves don’t exist in fluids
• Body waves
Rayleigh waves
(long+transverse waves)
Particles in elliptical paths. Ellipses
width decreases with increasing depth
Change from depth>1/5 of λ
D. Bard / VTAF01 / 19 Jan. 2016
Wave phenomena
• Interferences: constructive / destructive
• Standing waves
p− x, t = p cos(ωt − kx)
p+ x, t = p cos(ωt + kx)p x, t = p− x, t + p+ x, t = 2 p sin(kx)cos ωt
Position-dependent amplitude
oscillating according to cos(ωt)Two travelling waves propagating in
opposite directions
p1 x, t = p cos(ωt − kx)
p2 x, t = p cos(ωt − kx + θ)p x, t = p1 x, t + p2 x, t = 2 pcos
θ
2sin(ωt − kx + θ)
Constructive/destructive
depending on Ф
D. Bard / VTAF01 / 19 Jan. 2016
Outline
Course Information
Introduction to Acoustics
Administration
Summary
Wave propagation
D. Bard / VTAF01 / 19 Jan. 2016
Summary
• Course introduction
• Basics of acoustics
• Wave propagation
REFERENCES: Animations retrieved from Dan Russell’s website
