Читать книгу Engineering Acoustics - Malcolm J. Crocker - Страница 100

The sound power W of a sound source is given by integrating the intensity over any imaginary closed surface S surrounding the source (see Figure 3.7):

(3.41)

Figure 3.7 Imaginary surface area S for integration.

The normal component of the intensity I_n must be measured in a direction perpendicular to the elemental area dS. If a spherical surface, whose center coincides with the source, is chosen, then the sound power of an omnidirectional (monopole) source is

(3.42)

(3.43)

and from Eq. (3.35) the sound power of a monopole is [4, 13]

(3.44)

It is apparent from Eq. (3.44) that the sound power of an idealized (monopole) source is independent of the distance r from the origin, at which the power is calculated. This is the result required by conservation of energy and also to be expected for all sound sources.

Equation (3.43) shows that for an omnidirectional source (in the absence of reflections) the sound power can be determined from measurements of the mean square sound pressure made with a single microphone. Of course, for real sources, in environments where reflections occur, measurements should really be made very close to the source, where reflections are presumably less important.

The sound power of a dipole source is obtained by integrating the intensity given by Eq. (3.40) over a sphere around the source. The result for the sound power is

(3.45)

The dipole is obviously a much less efficient radiator than a monopole, particularly at low frequency.