THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

276 11. Acoustics of Enclosed Spaces: Architectural Acousticsparticular the autocorrelation function (ACF) that contains the same informationas power density spectrum but it is adjusted to account for hearing sensitivity.Effective duration of the normalized ACF is defined by the delay τ e at which theenvelope of the normalized ACF becomes one-tenth of its maximal value. Theresponse of the ear includes the effects of time delay due not only to the room’sacoustical characteristics, but also the spatially incurred differences in the signalsreaching the right and the left ears. The difference in the sounds arriving at theear is measured by the “interaural cross-correlation function” or IACF, which isdefined byIACF(τ) =∫ t2t 1p L (t)p R (t + τ)√ ∫ t2∫ (11.25)p 2 t2L t 1p 2 R dtwhere L and R denotes entry to the left and right ears, respectively. The maximumpossible value of IACF is unity. The time t = 0 is the time of the arrival of thedirect sound from the impulse radiated by a source. Integration from 0 to t 2 msincludes the energy of the direct sound and any early reflections and reverberantsounds occurring during the t 2 interval. Because there is a time lapse of about 1 msfor a sound wave to impinge the other side of the ear after impinging one side, itis customary to vary τ over the range from –1 ms to +1 ms. In order to obtain asingle number that measures the maximum similarity of all waves arriving at thetwo ears with the time integration limits and the range of τ, it is customary to choosethe maximum value of IACF, which is then called the interaural cross-correlationcoefficient (IACC), i.e.t 1IACC = |IACF(t)| maxDifferent integration periods are used for IACC. The standard ones includeIACC A (t 1 = 0 to t 2 = 1000 ms), and IACC E(arly) (0–80 m), IACC L(ate) (80–1000 m). The early IACC is a measure of the apparent source width ASW and thelate IACC is a measure of the listener envelopment LEV. IACC is generally measuredby recording on a digital tape recorder the outputs of two tiny microphoneslocated at the entrances to the ear canals of a person or a dummy head, and quantifyingthe two ear differences with a computer program that performs the operationof Equation (11.25). IACC A is determined with a frequency bandwidth of 100 Hz–8 kHz and for a time period of 0 to about 1 s.Subjective attributes for a sound field in a room have been developed experimentallywith actual listeners. The simplest sound field is considered first, a situationwhich consists of the direct sound and a single reflection acting in lieu of a setof reflections. The data obtained are based on tests in anechoic chambers (whichallowed for simulation of different concerts halls) with normal hearing subjectslistening to different musical motifs. From these subjective tests the optimum designobjectives are established, namely the listening level, preferred delay time,