Loudspeakers 677It is apparent that the intensity level IL will equal the sound pressure level SPL only if
po C 400 Rayls. For particular combinations of temperature and static pressure this will
be true, but under “ standard measuring conditions ” of
TP 22 °C and 0 751 mm Hg, PC 0 407 Rayls. (23.6)The error of –0.1 dB can be neglected for practical purposes.
23.2 Characteristic Impedance ......................................................................................
The characteristic impedance is the ratio of the effective sound pressure to the particle
velocity at that point in a free, plane, progressive sound wave. It is equal to the product of
the density of the medium times the speed of sound in the medium ( p 0 C ). It is analogous
to the characteristic impedance of an infi nitely long, dissipation-less, transmission line.
The unit is the Rayl, or Newton s/m^3.
23.3 Radiation Impedance.............................................................................................
When a vibrating diaphragm is placed in contact with air, its impedance to motion is
altered; the added impedance seen by the surfaces that emit useful sound energy is termed
“ radiation impedance. ” The radiation reactance is usually positive, corresponding to an
apparent mass. Both refl ective mass and resistance as seen by the diaphragm depend on
its size, shape, frequency, and the acoustical environment in which it radiates.
23.4 Radiation from a Piston.........................................................................................
Many radiating sources can be represented by the simple concept of a vibrating piston
located in an infi nitely large rigid wall. The piston is assumed to be rigid so that all parts
of its surface vibrate in phase and its velocity amplitude is independent of the mechanical
or acoustic loading on its radiating surface.
Figure 23.1 shows the problem: we wish to know the sound pressure at a point A located
distancer and angle θ from the center of the piston. To do this, we divide the surface of
the piston into a number of small elements, each of which is a simple source vibrating
in phase with all the other elements. The pressureA is, then, the sum in magnitude and