Lecture Summary Chapter 2 Summation

Transcription

1 Lecture Summary Chapter 2 Summation stable summation criteria o matched origin o may have unlimited multiple inputs o may arrive from different directions o must have significant overlap duration adding db SPL o see slide for formula o note simplifications that may be applicable relative level effects phase wheel response ripple o time offset shifts all frequency by same amount of time o time offsets shift all frequencies by a different amount of phase o result of summation with time offset (of signals at same frequency) is response ripple Level Offset Effects L e v e l C h a n g e ( d B ) Level Offset Max Peak Height Max Null Depth Max Ripple 1

2 summation zones defined o coupling sources with ±1/3 wavelength (± 120º) amount of addition ranges 0 to 6 db depending on phase/level offset ripple is ±3 db most easily achieved at low frequencies due to large wavelengths o cancellation evil twin of coupling zone effects only subtractive phase offset ±150º to ±180º ripple ±50 db o combing zone phase offset reaches point where subtraction begins (> ±120º) less than 4 db level difference dips and peaks ripple ranges from ±6 db to ±50 db avoid! highest form of variance over frequency o combining zone level offset ranges from 4 db to 10 db semi-isolated state relative to sources (limits magnitude of dips/peaks) ripple no more than ±6 db o isolation zone 10 db or more of level offset (think lute and bagpipes playing a duet ) interactions generally negligible relative phase has nominal effect ripple does not exceed 6 db 2

3 McCarthy s summation zone icons and reference chart comb filtering effects 3

4 application loudspeaker mounted in rigid (undamped) pipe o note how sound propagates at low frequencies o calculate wavelength of acoustic signal and phase shift that occurs as wave traverses pipe if operated at 150 Hz o calculate level of combined (summed) signal at source (need general formula) o if operating frequency changed to 100 Hz, determine change in summed signal at source o what have we ignored (and would need to include for a complete analysis)? resonance of pipe inverse square law effects for radiation outside the pipe losses traversing pipe (generally negligible) application flanging vs. phasing o flanging = swept delay creates fixed space notches may have non-musical consequences best effect on inharmonic/non-periodic sounds (e.g., symbols) o phaser modulate a set of non-uniformly spaced notches realized with string of allpass filters phase of individual frequency components modulated 4

5 response ripple: spatial distribution o time offsets vary over the space o relationship between courses and summation destination is triangular o different types of triangles reveal the spatial variation tendencies isosceles right obtuse acute factors affecting response at summation point o level offset due to distance offset (inverse square law) o level offset due to polar response (frequency and angular dependent) o phase offset due to path length difference our Pythagorean problem level offset is ratio, time offset is difference summation example key features o maximum addition over all frequencies at center of isosceles triangle (coupling zone) o 1 KHz and 10 KHz show deep cancellations around right triangle point (combing) o 10 KHz is first to show reduced combing as move into obtuse triangle (isolation zone) o area inside isosceles triangle (acute) has highest degree of variation over position/frequency (combing) o isolation increases as obtuse angle increases o 100 Hz pattern does not show cancellation at the right angle position (displacement between sources is less than a wavelength) 5

6 acoustic crossover o meeting point of two (or more) correlated input signals at comparable levels o separated by frequency in the same (or separate) enclosure o separated over a matched range in separate enclosure o separated by a physical boundary (in a room) divider/crossover terminology o spectral divider electronic device that separates the response into multiple frequency bands for transmission through distinct loudspeakers ( crossover network, which can be active or passive) o spectral acoustic crossover frequency range where equal acoustic levels are found from each of the electronically/physically separated elements that converge there o spatial divider electronic or acoustic device that separates response into multiple channels of common frequency range for transmission through distinct loudspeakers (typically aimed in different directions) o spatial acoustic divider location where equal acoustic levels are found from the multiple electronically/physically separated elements that converge there acoustic crossover quantification o crossover class overlap unity gap o crossover slope (order) 1 st (6 db/octave) 2 nd (12 db/octave) 3 rd (18 db/octave) o symmetry levels class o number of elements o combined response 6

7 application spectral crossover in two-way system 7

8 choosing a spatial crossover phase alignment point 8

9 spectral vs. spatial crossovers o common ground interactions governed by properties of acoustic summation strategies for achieving optimal summation based on phase-aligned crossover o differences spatial crossover can run through full audio range much more difficult to isolate with cancellation relative phase in a spatial divider affects all frequencies, while phase change in spectral divider only affects frequency range of crossover o analogous functions ( duality ) position in room where two speakers share equal level is analogous to spectral divider crossover frequency (coupling zone) directional control capability of speaker analogous to spectral divider slope highly directional speaker is like a steep spectral crossover change in relative level between speakers becomes a change in position of the spatial crossover point analogous to crossover frequency shift in spectral divider that results from changing the relative driver level power addition capability that comes from H/V overlap in the spatial crossover analogous to usable overlap in the crossover frequency of spectral divider 9

10 spatial crossover classes o gap: A+B < 0 db o unity: A+B = 0 db o overlap: A+B > 0 db multiway 10

11 speaker array types SPL map legend 11

12 coupled line source crossover class progressions coupled point source array crossover class progressions o unique feature: can maintain unity class crossover over distance done by creating unity splay angle not automatic variable over frequency 12

13 uncoupled line source crossover class progressions uncoupled point source crossover class progressions 13

14 uncoupled point destination crossover class progressions speaker/room summation o room reflections are correlated to source signal o reflections can continue for extended periods o most surfaces do not reflect all frequencies at the same level/phase/angle of incidence o distance between speaker and surface analogous to half the source displacement distance between two array elements o relative angle of speaker and surface analogous to half the splay angle between two array elements o coverage angle of reflected virtual speaker is same as coverage angle of source speaker o room surface is the spatial crossover (coupling zone) o absorption of wall surface analogous to level reduction / asymmetrical crossover o power addition capability from H/V overlap analogous to couple zone addition 14

15 application loudspeaker enclosure types o infinite baffle o sealed box o bass reflex o passive radiator o compound/band-pass o front-loaded horn 15

16 o rear-loaded horn o transmission line / labyrinth o damped pipe / tapered tube Use of tapering and/or acoustic absorption material can increase the effective length of the pipe 16