COURSE YEAR: 2020/2021
15-4-2021
7LS8M0 ARCHITECTURAL ACOUSTICS
SUMMARY OF ALL LECTURES (AND KUTRUFF BOOK) REGARDING THIS COURSE
BY: F.M. ARNTS
STUDENT AT TU EINDHOVEN
, 7LS8M0 Architectural Acous�cs
TABLE OF CONTENTS
FUNDAMENTALS OF ACOUSTICS ...................................................................................................................................3
LECTURE F.1...............................................................................................................................................................3
Harmonic mo�on ..................................................................................................................................................3
Complex numbers .................................................................................................................................................3
Impedance ............................................................................................................................................................4
Resonance .............................................................................................................................................................4
LECTURE F.2...............................................................................................................................................................5
Acous�c power .....................................................................................................................................................5
Fourier transform..................................................................................................................................................5
Impulse response g(t) ...........................................................................................................................................6
KUTRUFF CHAPTER 2 SOME FACTS ON MECHANICAL VIBRATIONS ..........................................................................6
LECTURE F.3...............................................................................................................................................................7
Wave equa�on in fluids ........................................................................................................................................7
Harmonic waves....................................................................................................................................................8
Intensity ................................................................................................................................................................8
LECTURE F.4...............................................................................................................................................................8
Sound pressure level .............................................................................................................................................8
Elas�c stresses on a solid element ........................................................................................................................9
KUTRUFF CHAPTER 3 ACOUSTIC VARIABLES AND BASIC RELATIONS ........................................................................9
KUTRUFF CHAPTER 4.1 AND 4.2 PLANE WAVES, ATTENUATION ..............................................................................9
LECTURE F.5 & F.6 ...................................................................................................................................................10
Acous�c atenua�on ...........................................................................................................................................10
Spherical waves...................................................................................................................................................12
Sound radia�on...................................................................................................................................................12
KUTRUFF CHAPTER 4 PLANE WAVES, ATTENUATION .............................................................................................13
KUTRUFF CHAPTER 5 SPHERICAL WAVE AND SOUND RADIATION .........................................................................13
ENVIRONMENTAL ACOUSTICS .....................................................................................................................................15
LECTURE E.1 & E.2 ...................................................................................................................................................15
Reflec�on ............................................................................................................................................................15
Refrac�on............................................................................................................................................................18
LECTURE E.3 & E.4 ...................................................................................................................................................19
Diffrac�on ...........................................................................................................................................................19
Scatering ............................................................................................................................................................20
KUTRUFF CHAPTER 6 REFLECTION AND REFRACTION.............................................................................................22
1
, 7LS8M0 Architectural Acous�cs
KUTRUFF CHAPTER 7 DIFFRACTION AND SCATTERING ...........................................................................................22
BUILDING ACOUSTICS ..................................................................................................................................................23
LECTURE B.1 ............................................................................................................................................................23
Sound waves in isotropic solids ..........................................................................................................................23
Sound waves in unbounded solids ......................................................................................................................23
Reflec�on and refrac�on, Rayleigh wave ...........................................................................................................25
Wave in plates and bars ......................................................................................................................................26
LECTURE B.2 ............................................................................................................................................................29
Building acous�cs................................................................................................................................................29
Characteriza�on and measurement ...................................................................................................................29
Single leaf par��ons ...........................................................................................................................................30
Double leaf par��ons .........................................................................................................................................31
KUTRUFF CHAPTER 10 SOUND WAVES IN ISOTROPIC SOLIDS ................................................................................32
KUTRUFF CHAPTER 14 BUILDING ACOUSTICS .........................................................................................................33
LECTURE B.3 ............................................................................................................................................................33
Sound reduc�on index combining mul�ple surfaces..........................................................................................33
Flanking sound transmission ...............................................................................................................................34
ROOM ACOUSTICS .......................................................................................................................................................36
LECTURE R.1 ............................................................................................................................................................36
Introduc�on ........................................................................................................................................................36
Acous�cs design ..................................................................................................................................................36
LECTURE R.2 CONCERT HALL ...................................................................................................................................37
Impulse response measurement ........................................................................................................................37
Roomacous�c parameters ..................................................................................................................................38
Speech transmission index..................................................................................................................................40
LECTURE R.3 ............................................................................................................................................................41
Room acous�cs in small rooms ...........................................................................................................................41
Experiment: how do room modes behave in the tu labaratory?........................................................................42
Sound absorp�on ................................................................................................................................................42
KUTRUFF CHAPTER 9 SOUND IN CLOSED SPACES ...................................................................................................44
KUTRUFF CHAPTER 13 ROOM ACOUSTICS ..............................................................................................................44
2
, 7LS8M0 Architectural Acous�cs
FUNDAMENTALS OF ACOUSTICS
LECTURE F.1
HARMONIC MOTION
Harmonic mo�on = periodic mo�on with the same amplitude (e.g. mass-spring system).
Cosine func�on harmonic.
TIME AVERAGED SIGNAL
Integrate harmonic mo�on over �me. The displacement is squared, otherwise we would get just 0.
t0 = sufficiently long �me interval.
COMPLEX NUMBERS
The displacement s(t) can be writen as a complex number, with ‘e’ = complex exponen�al.
The physical signal is the real value of the complex signal:
𝑠𝑠̂ = |s| = amplitude of the signal
ωt + ϕ = phase of the signal
Real part = the projec�on on the x
axis = 𝑠𝑠̂ ∙ cos (ωt + φ)
Imaginary part = the projec�on on
the y axis = 𝑠𝑠̂ ∙ sin (ωt + φ)
3
15-4-2021
7LS8M0 ARCHITECTURAL ACOUSTICS
SUMMARY OF ALL LECTURES (AND KUTRUFF BOOK) REGARDING THIS COURSE
BY: F.M. ARNTS
STUDENT AT TU EINDHOVEN
, 7LS8M0 Architectural Acous�cs
TABLE OF CONTENTS
FUNDAMENTALS OF ACOUSTICS ...................................................................................................................................3
LECTURE F.1...............................................................................................................................................................3
Harmonic mo�on ..................................................................................................................................................3
Complex numbers .................................................................................................................................................3
Impedance ............................................................................................................................................................4
Resonance .............................................................................................................................................................4
LECTURE F.2...............................................................................................................................................................5
Acous�c power .....................................................................................................................................................5
Fourier transform..................................................................................................................................................5
Impulse response g(t) ...........................................................................................................................................6
KUTRUFF CHAPTER 2 SOME FACTS ON MECHANICAL VIBRATIONS ..........................................................................6
LECTURE F.3...............................................................................................................................................................7
Wave equa�on in fluids ........................................................................................................................................7
Harmonic waves....................................................................................................................................................8
Intensity ................................................................................................................................................................8
LECTURE F.4...............................................................................................................................................................8
Sound pressure level .............................................................................................................................................8
Elas�c stresses on a solid element ........................................................................................................................9
KUTRUFF CHAPTER 3 ACOUSTIC VARIABLES AND BASIC RELATIONS ........................................................................9
KUTRUFF CHAPTER 4.1 AND 4.2 PLANE WAVES, ATTENUATION ..............................................................................9
LECTURE F.5 & F.6 ...................................................................................................................................................10
Acous�c atenua�on ...........................................................................................................................................10
Spherical waves...................................................................................................................................................12
Sound radia�on...................................................................................................................................................12
KUTRUFF CHAPTER 4 PLANE WAVES, ATTENUATION .............................................................................................13
KUTRUFF CHAPTER 5 SPHERICAL WAVE AND SOUND RADIATION .........................................................................13
ENVIRONMENTAL ACOUSTICS .....................................................................................................................................15
LECTURE E.1 & E.2 ...................................................................................................................................................15
Reflec�on ............................................................................................................................................................15
Refrac�on............................................................................................................................................................18
LECTURE E.3 & E.4 ...................................................................................................................................................19
Diffrac�on ...........................................................................................................................................................19
Scatering ............................................................................................................................................................20
KUTRUFF CHAPTER 6 REFLECTION AND REFRACTION.............................................................................................22
1
, 7LS8M0 Architectural Acous�cs
KUTRUFF CHAPTER 7 DIFFRACTION AND SCATTERING ...........................................................................................22
BUILDING ACOUSTICS ..................................................................................................................................................23
LECTURE B.1 ............................................................................................................................................................23
Sound waves in isotropic solids ..........................................................................................................................23
Sound waves in unbounded solids ......................................................................................................................23
Reflec�on and refrac�on, Rayleigh wave ...........................................................................................................25
Wave in plates and bars ......................................................................................................................................26
LECTURE B.2 ............................................................................................................................................................29
Building acous�cs................................................................................................................................................29
Characteriza�on and measurement ...................................................................................................................29
Single leaf par��ons ...........................................................................................................................................30
Double leaf par��ons .........................................................................................................................................31
KUTRUFF CHAPTER 10 SOUND WAVES IN ISOTROPIC SOLIDS ................................................................................32
KUTRUFF CHAPTER 14 BUILDING ACOUSTICS .........................................................................................................33
LECTURE B.3 ............................................................................................................................................................33
Sound reduc�on index combining mul�ple surfaces..........................................................................................33
Flanking sound transmission ...............................................................................................................................34
ROOM ACOUSTICS .......................................................................................................................................................36
LECTURE R.1 ............................................................................................................................................................36
Introduc�on ........................................................................................................................................................36
Acous�cs design ..................................................................................................................................................36
LECTURE R.2 CONCERT HALL ...................................................................................................................................37
Impulse response measurement ........................................................................................................................37
Roomacous�c parameters ..................................................................................................................................38
Speech transmission index..................................................................................................................................40
LECTURE R.3 ............................................................................................................................................................41
Room acous�cs in small rooms ...........................................................................................................................41
Experiment: how do room modes behave in the tu labaratory?........................................................................42
Sound absorp�on ................................................................................................................................................42
KUTRUFF CHAPTER 9 SOUND IN CLOSED SPACES ...................................................................................................44
KUTRUFF CHAPTER 13 ROOM ACOUSTICS ..............................................................................................................44
2
, 7LS8M0 Architectural Acous�cs
FUNDAMENTALS OF ACOUSTICS
LECTURE F.1
HARMONIC MOTION
Harmonic mo�on = periodic mo�on with the same amplitude (e.g. mass-spring system).
Cosine func�on harmonic.
TIME AVERAGED SIGNAL
Integrate harmonic mo�on over �me. The displacement is squared, otherwise we would get just 0.
t0 = sufficiently long �me interval.
COMPLEX NUMBERS
The displacement s(t) can be writen as a complex number, with ‘e’ = complex exponen�al.
The physical signal is the real value of the complex signal:
𝑠𝑠̂ = |s| = amplitude of the signal
ωt + ϕ = phase of the signal
Real part = the projec�on on the x
axis = 𝑠𝑠̂ ∙ cos (ωt + φ)
Imaginary part = the projec�on on
the y axis = 𝑠𝑠̂ ∙ sin (ωt + φ)
3
