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Hopefully a simple question. I was wondering what the blue line in this graph represents.

This is looking at loudspeaker modelling.

The red line is obviously the frequency response as loudspeakers are modelled as high pass filters.

Is the blue line meant to represent the phase?

enter image description here

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2 Answers 2

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Is the blue line meant to represent the phase?

Yes. If two speakers are "in phase" then it means as the cone goes outward on one, the same thing happens identically on the other. Thus, the sound fronts emerge from them simultaneously.

Since it is not possible to emit sound "early", all phases are negative (delayed.)

Now interesting things happen when speakers are repositioned. If one of these speakers is pushed back a few feet, then it's sound is going to hit your ear "late" - or you could say that it's phase is lagging when it reaches your ear. Even though both speakers are making the same sound, the position of the second one is causing a phase shift.

When two signals are "in-phase", their outputs add, and we perceive that as increased volume.

When two signals are not in phase, their outputs may add or subtract. From 0° to 89°, they add, with 90° being zero addition. From 91° to 179°, they subtract, with 180° being perfect cancellation (assuming perfect speakers in a perfect environment, which is impossible.) And from 181° to 359° they add again, with 0° being perfect addition again. (Note that because sound pressure is logarithmic, it takes 4x the power to achieve a 2x increase in loudness - so this 100% addition is not doubling the volume.)

So the two speakers, one pushed back, have introduced a delay. If you continue pushing that speaker backwards, you'll reach 180° and it will seem much quieter.

Now you're probably looking at the strange shape of the blue trace and thinking "How do speakers make meaningful sound at all then?" That's because the real world is full of walls and floors, couches and TV's, things to bounce that sound around from and result in a nearly infinite mix of impulses coming from every direction. So phase ends up mattering little for the average person in the typical home environment. Where phase is really important, is in sound reinforcement (events, concerts), audiophiles (gotta have "pure" sound), and "pro" speaker box construction.

If there's no output level at the low frequencies. What does the phase represent?

Most speakers are physically incapable of reproducing meaningful sound at ultra-low frequencies like <20Hz. But if this one did, then the phase plot would show you the expected delay. Basically, since the red line drops off near 30-40Hz, ignore the phase below that, since the speaker won't be reproducing it anyways.

Research group delay for even more info.

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  • \$\begingroup\$ Thanks, very interesting explanation :) \$\endgroup\$ Commented Feb 9, 2022 at 23:31
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Yes, red trace is for the amplitude response (left axis) and the blue for phase response (right axis).

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  • \$\begingroup\$ Thanks, what exactly does that mean in real terms? If there's no output level at the low frequencies. What does the phase represent? \$\endgroup\$ Commented Feb 9, 2022 at 21:50
  • \$\begingroup\$ resistive loads always have a zero phase, a inductor has +90°, a capacitor -90°. The phase tells you the timing relationship between voltage and current. As all real parts have parasitic components, phase also changes over frequency (some parasitics get more dominant, others less. Also, as a speaker uses a coil to generate the force for moving the membran, one can expect a speaker to show characteristics of an inductor). This is in terms of speakers important, if you want to combine coponents for a speaker. then you should also match / optimize phase \$\endgroup\$
    – schnedan
    Commented Feb 9, 2022 at 22:27

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