Building Acoustics

80 Building acoustics j( cos sin ) ii i j( cos sin ) i, 00 (, , ) ˆ e and ˆ (, , ) cos e. kx y kx y x pxy p p vxy c φφ φ φ φ φφ ...

Waves in fluid and solid media 81 (^222) stat 00 2()sincosd21Rp sincosd. ππ α ==−αφ φ φ φ ⎡⎤φ φ φ ∫∫⎢⎥⎣⎦ (3.79) Inserting for Rp ...

82 Building acoustics being independent of the angle of incidence. We also pointed out that this assumption is reasonably correc ...

Waves in fluid and solid media 83 ir t irt ir 11 2 2 cos cos cos or cos cos cos cos. vv v ppp pp ZZ Z Z φφψ φ φψ ψ += + −= = (3. ...

84 Building acoustics reflecting. The surface impedance for these lids is thereby infinite and the particle velocity is zero. Ou ...

Waves in fluid and solid media 85 0 00 (^022) 1 22 cos cos (,, ). nn n n ff x x cc pfxx C ff ππ ∞ = ⎛⎞⎛ ⎞ ⎜⎟⎜ ⎟⋅⋅ ⋅ = ⎝⎠⎝ ⎠ − ∑ ...

86 Building acoustics Figure 3.17 Relative sound pressure at a fixed position, x = 1.2 m, in the tube shown in Figure 3.16. Soli ...

Waves in fluid and solid media 87 wave propagation will occur, i.e. longitudinal stresses will produce lateral strains on the ou ...

88 Building acoustics It should be noted that using the particle velocity as a variable, which we have done in Equation (3.94) a ...

Waves in fluid and solid media 89 (^) S. G c ρ = (3.99) Using Equation (3.96), (3.98) and (3.99) we get for a plate S L 1 2 c c ...

90 Building acoustics constants for these panels. We shall give an example below (see section 3.7.3.3) and the reason is that fu ...

Waves in fluid and solid media 91 The quantity I is the cross sectional area moment of inertia of the plate per unit width. As m ...

92 Building acoustics Figure 3.19 Phase speed of bending waves in concrete slabs of thickness 50, 100, 150 and 200 mm. Thin line ...

Waves in fluid and solid media 93 In the literature, e.g. Blevins (1979), we find the eigenfunctions and eigenfrequencies listed ...

94 Building acoustics corresponding bending stiffness Bx and Bz. In several cases, one may apply the geometric average of the st ...

Waves in fluid and solid media 95 EExυzzx= υ. (3.111) The bending stiffness in the two directions will then be given by () () 3 ...

96 Building acoustics () 3 2 2 2 2 3 2 , 12 1 1 0.81 1 (^25) 1 2 and 1. 12 (1 ) x z xz Eh B H L EH h B H L Eh H B L π υ π υ = ⎛⎞ ...

Waves in fluid and solid media 97 example will, however, be on an input mobility, not a transfer mobility (the ratio of velocity ...

98 Building acoustics 3.7.3.5 Modal density for bending waves on plates Detailed frequency information is normally not required ...

Waves in fluid and solid media 99 If we wish to calculate the number of modes inside a given frequency interval Δω (or Δf), we j ...