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staggering crossover points
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<blockquote data-quote="thch" data-source="post: 2453246" data-attributes="member: 562032"><p>cycle -- one repetion.</p><p></p><p>for fun, (and because mathmatically its nice), lets say you've got a car. with wheels. and there is an air nozzel on each wheel.</p><p></p><p>so far so good, nothing complex. so lets drive the car at 5mph and look at the motion of the air nozzels. the air nozzels each move higher off the ground, and then move back down near the ground, then back up, ect... and they do this at a constant rate or "frequency". in this case, if you plot the vertical position of an air nozzel vs time, you'll get a "sine wave".</p><p></p><p>when the air nozzel is near the top of the wheel, turning it an extra 1/16th of a turn doesn't really move the nozzel much further up or down.</p><p></p><p>when the air nozzel is near the sides, turning it the extra 1/16th will move it significantly up or down.</p><p></p><p>thus a sine wave has somewhat flat peaks, and somewhat sharp transitions. (not as much as a square wave though).</p><p></p><p>ok. so lets say you have two wheels and two air spokes. both wheels are spinning at the same rate, and you plot the vertical position of EACH nozzel. both will give you sine waves.</p><p></p><p>now lets say that the air nozzel of the first tire started in the highest upward position, and the tire 2 nozzel pointed down. now as nozzel 1 is moving upward, nozzel 2 is moving downward! the two are not "in phase".</p><p></p><p>and if nozzel 1 started from the lowest point and nozzel 2 started at the mid point, the waves would not be in phase, but would also not be fully out of phase.</p><p></p><p>now it makes sense to replace "vertical position of nozzel" with "outward excursion of speaker", and suddenly there is a practical application -- the speaker is moving in and out at some frequency (for purpose of explaination).</p><p></p><p>lets concider that the speaker has mass. now when the amp starts to move the speaker cone. but when the amp wants to start moving the cone back, the cone wants to keep moving forward. eventually it will stop forward movement, and move backward, which is what the amp wanted. the same thing happens later when the amp wants the speaker to move forward -- the speaker keeps moving backwards.</p><p></p><p>similar things happen elsewhere in the audio system.</p><p></p><p>as for the plots, x is just "variable". it could be time or position or anything really. as x increases, the value of Sin(x) moves periodically from a low to high value. 120 is in degrees, and is 120*3.14/180 radians.</p></blockquote><p></p>
[QUOTE="thch, post: 2453246, member: 562032"] cycle -- one repetion. for fun, (and because mathmatically its nice), lets say you've got a car. with wheels. and there is an air nozzel on each wheel. so far so good, nothing complex. so lets drive the car at 5mph and look at the motion of the air nozzels. the air nozzels each move higher off the ground, and then move back down near the ground, then back up, ect... and they do this at a constant rate or "frequency". in this case, if you plot the vertical position of an air nozzel vs time, you'll get a "sine wave". when the air nozzel is near the top of the wheel, turning it an extra 1/16th of a turn doesn't really move the nozzel much further up or down. when the air nozzel is near the sides, turning it the extra 1/16th will move it significantly up or down. thus a sine wave has somewhat flat peaks, and somewhat sharp transitions. (not as much as a square wave though). ok. so lets say you have two wheels and two air spokes. both wheels are spinning at the same rate, and you plot the vertical position of EACH nozzel. both will give you sine waves. now lets say that the air nozzel of the first tire started in the highest upward position, and the tire 2 nozzel pointed down. now as nozzel 1 is moving upward, nozzel 2 is moving downward! the two are not "in phase". and if nozzel 1 started from the lowest point and nozzel 2 started at the mid point, the waves would not be in phase, but would also not be fully out of phase. now it makes sense to replace "vertical position of nozzel" with "outward excursion of speaker", and suddenly there is a practical application -- the speaker is moving in and out at some frequency (for purpose of explaination). lets concider that the speaker has mass. now when the amp starts to move the speaker cone. but when the amp wants to start moving the cone back, the cone wants to keep moving forward. eventually it will stop forward movement, and move backward, which is what the amp wanted. the same thing happens later when the amp wants the speaker to move forward -- the speaker keeps moving backwards. similar things happen elsewhere in the audio system. as for the plots, x is just "variable". it could be time or position or anything really. as x increases, the value of Sin(x) moves periodically from a low to high value. 120 is in degrees, and is 120*3.14/180 radians. [/QUOTE]
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