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Figure 4.16: Perceived level of tone burst rises with duration as resonance bulids up.
The HAS has evolved to offer intelligibility in reverberant environments which it does by averaging all received
energy over a period of about 30 milliseconds. Reflected sound which arrives within this time is integrated to
produce a louder sensation, whereas reflected sound which arrives after that time can be temporally discriminated
and is perceived as an echo. Microphones have no such ability which is why we often need to have acoustic
treatment in areas where microphones are used.
A further example of the finite time discrimination of the HAS is the fact that short interruptions to a continuous tone
are difficult to detect. Finite time resolution means that masking can take place even when the masking tone begins
after and ceases before the masked sound. This is referred to as forward and backward masking. [ 8 ]
As the vibration envelope is such a complicated shape, Moore and Glasberg have proposed the concept of
equivalent rectangular bandwidth to simplify matters. The ERB is the bandwidth of a rectangular filter which passes
the same power as a critical band. Figure 4.17 ( a) shows the expression they have derived linking the ERB with
frequency. This is plotted in (b) where it will be seen that one third of an octave is a good approximation. This is
about thirty times broader than the pitch discrimination also shown in (b).
Figure 4.17: Effective rectangular bandwidth of critical band is much wider than the resolution of the pitch
discrimination mechanism.
[ 7 ] Fletcher, H., Auditory patterns. Rev. Modern Physics , 12 , 47-65 (1940)
[ 8 ] Zwicker, E., Subdivision of the audible frequency range into critical bands. J. Acoust. Soc. Amer. , 33 , 248 (1961)
4.9 Beats
Figure 4.18 shows an electrical signal (a) in which two equal sine waves of nearly the same frequency have been
linearly added together. Note that the envelope of the signal varies as the two waves move in and out of phase.
Clearly the frequency transform calculated to infinite accuracy is that shown at (b). The two amplitudes are constant
 
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