Sound Transmission Loss of Panels

Abstract

In general, the noise level inside a building or structure is determined by the transmission of air-borne sound from external and internal acoustic sources and by structure-borne sound induced by some mechanical sources.

Problems

13.1

Calculate the radiation ratio $\bar{\sigma }_\mathrm{a}$ for an infinite plate, $\mu = 22$ kg/m$^{2}$ and $f_\mathrm{c}=720$ Hz, in the frequency range up to 500 Hz.

13.2

Determine how the sound transmission loss for a single leaf panel is changed if the thickness of the homogeneous plate is changed from $h_1$ to $h_2$. Consider the frequency intervals $f\ll f_\mathrm{c}$ and $f > f_\mathrm{c}$.

13.3

Show that

$$\sum \limits _l {\dfrac{1}{k^2 - k_{lmn}^2} = \dfrac{d}{2\lambda _{mn} \tan (\lambda _{mn}d)}}$$

For notations, see Sect. 13.3.

13.4

A stiff plate is mounted as shown in Fig. 13.22. Determine the mobility of the plate as function of the distance d between plate and bottom structure. The mass per unit area of the infinitely stiff plate is $\mu$ and its area S. The fluid in the cavity is air.

Fig. 13.22

Stiff plate coupled to cavity

13.5

Show that

$$Y_{mn} (a) = \dfrac{1}{[\lambda _{mn}\sin (\lambda _{mn} a)]^2}\left[ {\dfrac{\sin (2\lambda _{mn}a)}{2\lambda _{mn} a} + 1} \right] $$

can close to a maximum be expanded as

$$\left| {Y_{mn} (a)}\right| = \dfrac{1}{(ak_{0a}^2 )^2(\xi ^2 + \delta _2^2 /4)}$$

13.6

Solve

$$\Gamma = \oint {\dfrac{\mathrm{d}\xi }{(\xi ^2 +\delta _1^2 / 4)(\xi ^2 + \delta _2^2 /4)}}$$

Make the integration along a semi-circle in the upper half plane of the complex plane.

13.7

Show that the sound transmission loss is independent of boundary conditions for $f > f_\mathrm{c}$.

13.8

Follow the one-dimensional procedure for the clamped plate to indicate the solution for a simply supported plate.

13.9

Determine the sound transmission loss of a double construction consisting of two panels with a cavity between them. Assume that the acoustic field between the plates is diffuse.

13.10

Determine the double wall resonance frequency given in Eq. (13.130).

13.11

Determine the sound transmission loss of a structure with a water load on one side. Consider only normal incidence.

13.12

Show that the sound transmission loss for a panel between two rooms tends to the sound transmission loss of an infinite panel as the dimensions of the rooms becomes infinite.