00 Frequency ranges of typical sounds 233.08 Figure 8.6 shows typical ranges. It should be noted that the 246.94 fundamental frequencies of speech and music go only to about 4 kHz, but the harmonics may in some circumstances go well into the 261.63 10 to 20 kHz range, or maybe even higher. 277.18 It is of interest to take the example of a square wave (Figure 8.7). This consists of a fundamental together with, strictly, an infinite 293.66 number of harmonics of diminishing amplitude, as in Equation 8.14. 311.13 329.63 x = A sin + sin ( 3 + 349.23 (8.14) 369.99 392.00 In practice a good square wave is obtained with some thirty terms. 415.30 440.00 466.16 493.88 523.25 Harmonics are of course exact multiples of a fundamental fre- quency and the number and relative strengths of the various har- Figure 8.7 A square wave monics go some way towards giving a sound its individual quality. At least as important are the starting transients. These are additional frequencies, not in general related to the fundamental, which last for Square wave signals, or waveforms approaching them, can be a only a brief time at the start of a sound. It is probably true to say that serious source of interference because of the likely existence of high their duration is typically no more than about ten cycles of the frequencies. For example a square wave of 1kHz fundamental will fundamental. Thus in a sound of basic frequency 400Hz (period contain frequencies of 1kHz, 3kHz, 5kHz, etc. and the 21st har- 1/400=2.5mS) the starting transients would probably have died monic will be 21kHz, albeit of low amplitude. Piccolo Flute Double Bassoon Trumpet t Tuba Double Bass Violin Piano Human voice Frequency Hz Figure 8.6 Typical frequency ranges 8/10 Sound, speech and hearing Acoustics Very effective absorbers can be made by using 25mm of mineral wool, faced with perforated hardboard, and with some 150 to 8.5.1 Reverberation time 200mm of air space behind, the air space being divided with hard- board or even cardboard into nesting boxes 120 to 200mm sq