Читать книгу Engineering Acoustics - Malcolm J. Crocker - Страница 120

In enclosed spaces the wave acoustics approach is useful, particularly if the enclosed volume is small and simple in shape and the boundary conditions are well defined. In the case of rigid walls of simple geometry, the wave equation is used, and after the applicable boundary conditions are applied, the solutions for the natural (eigen) frequencies for the modes (standing waves) are found. See Refs. [23, 24], and chapter 6 in the Handbook of Acoustics [1] for more details. However, for large rooms with irregular shape and absorbing boundaries, the wave approach becomes impracticable and other approaches must be sought. The ray acoustics approach together with the multiple‐image‐source concept is useful in some room problems, particularly in auditorium design or in factory spaces where barriers are involved. However, in many cases a statistical approach where the energy in the sound field is considered is the most useful. See Refs. [25, 26] and also chapters 60–62 in the Handbook of Acoustics [1] for more detailed discussion of this approach. Some of the fundamental concepts are briefly described here.

For a plane wave progressing in one direction in a duct of unit cross‐section area, all of the sound energy in a column of fluid c metres in length must pass through the cross‐section in one second. Since the intensity 〈I〉_t is given by p²_rms /ρc, then the total sound energy in the fluid column c metres long must also be equal to 〈I〉_t. The energy per unit volume ε (joules per cubic metre) is thus

(3.69)

or

(3.70)

The energy density ε may be derived by alternative means and is found to be the same as that given in Eq. (3.69) in most acoustic fields, except very close to sources of sound and in standing‐wave fields. In a room with negligibly small absorption in the air or at the boundaries, the sound field created by a source producing broadband sound will become very reverberant (the sound waves will reach a point with equal probability from any direction). In addition, for such a case the sound energy may be said to be diffuse if the energy density is the same anywhere in the room. For these conditions, the time‐averaged intensity incident on the walls (or on an imaginary surface from one side) is

(3.71)

or

(3.72)

In any real room, the walls will absorb some sound energy (and convert it into heat).