686 Chapter 23
Figure 23.8 shows the necessary peak amplitude of a piston mounted in an infi nite baffl e to
radiate one acoustic watt of sound power at various frequencies (one side only of the piston
radiating). Peak amplitudes in millimeters are marked on the family of curves. For any
other value of acoustic power output ( P ), multiply peak amplitude by VP. With an average
room of 2000 ft^3 , a reverberation time of 1 s, and a sound pressure level of 94 dB, the
total sound output power is of the order of 30 mW. To radiate this power at 50 Hz, the peak
amplitude of a 250-mm radiator will be about 2 mm, while a 100-mm piston to radiate
the same power would require a peak displacement of just over 13 mm. Even with “ long
throw ” loudspeakers, it is not possible to obtain a peak-to-peak displacement of 26 m m ,
thus the sound power capabilities must be severely limited at low frequencies. One will
often see response curves of these small speakers taken to apparently extraordinarily low
frequency limits, but these are always undertaken at low power input levels.
The directional radiation characteristics of a diaphragm are determined by the ratio of
the wavelength of the emitted sound to the diaphragm diameter. Increasing the ratio of
diaphragm diameter to wavelength decreases the angle of radiation. At frequencies in
which the wavelength is greater than four times the diaphragm diameter, the radiation can
be considered substantially hemispherical, but as this ratio decreases, the radiation pattern
narrows. Figure 23.9 shows the polar response of a piston in terms of the ratio of diameter
5002001005020Dia. mmDisplacement mm10 Hz 100 Hz 1000 Hz200 100 50 20 10 521Figure 23.8 : Peak amplitude of a piston to radiate 1 W.