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PART II Microphones FIGURE 3.3 Sound intensity variation with distance over a fixed solid angle. The intensity at any distance r from the source is given by: I W/4 r 2 (3.3) The effective sound pressure in pascals at that distance will be: p I 0 c (3.4) where 0 c is the specific acoustical impedance of air (405 SI rayls). For example, consider a point source of sound radiating a power of one watt uniformly. At a distance of 1 meter the intensity will be: 66 I 1 / 4 ( 1 ) 2 1 / 4 0 . 08 W/m 2 The effective sound pressure at that distance will be: p ( 0 . 08 ) 405 5 . 69 Pa RELATIONSHIP BETWEEN AIR PARTICLE VELOCITY AND AMPLITUDE The relation between air particle velocity ( u ) and particle displacement ( x ) is given by: u ( t ) j ( t ) (3.5) where 2 f and x ( t ) is the maximum particle displacement value. The complex operator j produces a positive phase shift of 90°. Some microphones, notably those operating on the capacitive or piezoelectric principle, will produce constant output when placed in a constant amplitude sound field. In this case u ( t ) will vary propor- tional to frequency. Other microphones, notably those operating on the magnetic induct ion principle, will produce a constant output when placed in a constant velocity sound field. In this case, x ( t ) will vary inversely proportional to frequency. THE DECIBEL We do not normally measure acoustical intensity; rather, we measure sound pressure level. One cycle of a varying sinusoidal pressure might look like that shown in Figure 3.4(a) . The peak value of this