Acoustics (VTAF05) - LTH fileAcoustics (VTAF05) JUAN NEGREIRA, ... D. Bard / Akustik VTAF05 / 3 Nov....

Acoustics (VTAF05)

JUAN NEGREIRA, DELPHINE BARD

DIVISION OF ENGINEERING ACOUSTICS, LUND UNIVERSITY

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

Outline

Course Information

Wave propagation

Introduction to Acoustics

Summary

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

Teachers

• Lectures:

‒ Delphine Bard, KC-building (3rd floor)

‒ Juan Negreira, KC-building (3rd floor)

‒ Anders Sjöström

• Exercises:

‒ Juan Negreira

• Laboratory:

‒ Juan Negreira

‒ Marie-Laure Divoux

• Administration:

– Christina Glans, KC-building (3rd floor)

Course responsibles

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

Course material

• Handed out material

– Lecture notes

– Exercise material

– Laboration instructions

– Project task

– Formulae

• Website (course material will be uploaded here):

http://www.akustik.lth.se/utbildning/kurser/

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

Laboratories & Project taskLaboratories

• Three Lab sessions (in groups of 2-3 students)

1. Recording, calibration and evaluation of sound

2. Room acoustics

3. Wind turbine noise

• Approximately 2 hours on site

– Preparation and post-processing time needed

• Results presented in form of a report

– Either passed or returned for completion

Project Tasks

• Performed in groups of 2-3 students

• Presented Friday, December 18th at 13:00-15:00

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

Examination

The final grade will be obtained as follows…

• Written exam (50 %)

– Thursday 15/1 at 8.00-13.00 in MA:8C

– Theoretical questions and exercises

– Calculator and handed out formulae summary allowed

– Graded: u, 3, 4, 5

• Project task (50 %)

– Graded: u, 3, 4, 5

• Executed laborations with passed reports

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

The course

• Time:

– 6 h/week of lectures and exercises (Tuesdays and Fridays)

– 6 h laboratory exercises off-schedule

• Purpose

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

Outline

Course Information

Wave propagation

Introduction to Acoustics

Summary

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

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

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

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

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

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

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

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)

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

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

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

Hearing process

• Pressure waves

• For a sound to be perceived

‒ Frequency: 20 Hz – 20 kHz

‒ Sound pressure level (SPL): frequency dependent

• Inner ear detects: ∆p ϵ [20 μPa, 200 Pa] wide range

‒ Use of logarithmic scale (in decibels)

Source Conveying medium Receptor

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

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)

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

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

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

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?

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

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

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

Frequency weightings (II)

• Filters and calculation

Lweighted = 10 log 10(Ln+weighting)

10

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

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

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

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

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

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

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

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

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

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

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

Regulations – environmental noise

• Infrastrikturprop.

1996/97:53

• Noise-maps

Location Measure Road Track Flight

Indoors LAeq,24h 30 30 30

Indoors LAFmax 45 45 45

Outside (façade) LAeq,24h 55 60 55

Outside LAFmax 70 70 70

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

Malmö – actions for noise exposure 2014

• Citizens exposed to >30 dBA indoors: 48 000,

>55 dBA outdoors: 126 000.

• Estimated cost (incl. health care and loss of work): 1 100 MSEK

• Proposed long term measures (250 MSEK):

– Source: Lower speed limit, silent asphalt,

driving style and silent car/tires

– Sound reduction: Noise barriers,

allowance for improvement of

sound reduction at dwellings

– Focus on sensitive places, e.g.

schools, pre-schools and parks

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

Outline

Course Information

Wave propagation

Introduction to Acoustics

Summary

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

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

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

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

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

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

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

Waves in fluid media (II)

Time and position dependency: p x, t = p+ cos ωt − kx = p+e−i(ωt−kx)

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

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

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

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

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

Outline

Course Information

Wave propagation

Introduction to Acoustics

Summary

J. Negreira, D. Bard / Akustik VTAF05 / 3 Nov. 2015

Summary

• Course introduction

• Basics of acoustics

• Wave propagation

REFERENCES: Animations retrieved from Dan Russell’s website

Thank you for your attention!

juan.negreira@construction.lth.se