Building Acoustics

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CHAPTER 1 Oscillating systems. Description and analysis 1.1 INTRODUCTION Sound and vibration are dynamic phenomena, generally re ...

2 Building acoustics physical phenomena and/or based on observations of the oscillatory motion we may in this case predict the f ...

Oscillating systems 3 MLS (maximum length sequences) which are binary sequences repeating themselves exactly. Measurements may t ...

4 Building acoustics function analysis, requires two-channel instruments. When performing so-called modal analysis, where the pu ...

Oscillating systems 5 0 0 0 0 1 ()d, 2 ()cos2 d 2 and ( ) sin 2 d. T T k T kk axtt T axt ft T bxt ft T π π = = = ∫ ∫ ∫ kt t k) ( ...

6 Building acoustics our physical measurement variables will always be functions of the positive frequencies. Note the symmetry ...

Oscillating systems 7 where crms denotes the RMS-value of the harmonic components. Using the complex form of Equation (1.6) we g ...

8 Building acoustics 1.4.1.2 Frequency analysis of a periodic function (periodic signal) An example of a periodic function is sh ...

Oscillating systems 9 1.4.2.1 Energy in transient motion Again letting x(t) represent the time history of the sound pressure in ...

10 Building acoustics -50 -40 -30 -20 -10 0 10 20 30 40 50 Time (ms) 0 25 50 75 100 125 150 x( t) Pulse duration T= 10 ms T= 1 m ...

Oscillating systems 11 viscous damping small enough to make it oscillate. We assume that x(t) is the displacement of the mass wh ...

12 Building acoustics 1 10 100 1000 Frequency (Hz) 1.0E-004 1.0E-003 1.0E-002 1.0E-001 1.0E+000 |X (f )| a=1 s-1 a=50 s-1 Figure ...

Oscillating systems 13 xt t()d +∞ −∞ ∫ =∞, which means that the Fourier transform according to Equation (1.13) does not exist. 0 ...

14 Building acoustics important function used to characterize stochastic functions in the frequency domain, the power spectral d ...

Oscillating systems 15 x(t) Time, t Δt Figure 1.10 Sampling of a continuous signal by time intervals Δt. x(t) Time, t x 0 x 1 x ...

16 Building acoustics (^1) j2 0 1 () 0,1,2,3,..., N kn N kn n XXkf xe k N N − − π = = Δ=∑ = − 1 , (1.21) where Δf is 1/T. The di ...

Oscillating systems 17 wheels or gears together with stochastic components from turbulent flow of air or water in the cooling sy ...

18 Building acoustics have a bandwidth Δf ≈ 0.71⋅ f 0 and a one-third-octave band a bandwidth Δf ≈ 0.23⋅ f 0. As mentioned above ...

Oscillating systems 19 Applying DFT analysis however, we see that the sound (or noise), being mainly stochastic, also contain pe ...