Building Acoustics

88 Building acoustics

It should be noted that using the particle velocity as a variable, which we have done
in Equation (3.94) and also further on, is just a choice. A corresponding equation for e.g.
the displacement could be used as well. The phase speed of the longitudinal wave,
according to the equations above, will be given by

()

L 2.

1

E

c

ρυ

=

−

(3.96)

Examples of data for common materials are given in Table 3.1, which we may use to
calculate the wave speed for longitudinal waves. It should be noted that wave speed
normally found in tabled data applies to pure longitudinal waves, i.e. calculated from the
formula (E/ρ)1/2. The loss factor given in the table applies to the internal energy losses in
the material.

Table 3.1 Examples of material properties.

Material

Density

kg/m^3

E-modulus^1

109 Pa

Poisson’s

ratio

Loss factor

ηint⋅ 10 -3

Steel 7700–7800 190–210 0.28–0.31 ~ 0.1

Aluminium 2700 66–72 0.33–034 ~ 0.1

Glass 2500 60 - 0.6–2.0

Concrete 2300 32–40 0.15–0.2 4–8

Concrete

(lightweight aggregate)

400–600 1.0–2.5 ~ 0.2 10–20

Concrete

(autoclaved aerated)

1300 3.8^2 ~ 0.2 10–20

Gypsum plate (plasterboard) 800–900 4.1 ~ 0.3 10–15

Chipboard 650–800 3.8 ~ 0.2 10–30

Fir, spruce 400–700 7–12 ~ 0.4 8–10

1 Dynamic E-modulus.^2 E-modulus for static pressure.

3.7.2 Shear waves

In a pure shear wave, also referred to as a transverse wave, we only get shear
deformations and no change of volume (see b) in Figure 3.18). The particle movements
are normal to the direction of wave propagation, and the wave equation for free wave
motion will be analogous to Equation (3.94), i.e.

22

22 0,

G vvyy

xt

ρ

∂∂

− =

∂∂

(3.97)

where vy represents the particle velocity normal to the direction of propagation. The shear
modulus is given by

,
2(1 )

E

G

υ

=

+

(3.98)

and for the phase speed cS we get