There is only some very minor frequency dependence of the speed of sound.
Thanks for the information. But that was not the core of the discussion and not what Prof. Klippel meant by the temperature-induced phase shift.
For a minimum phases system it cannot get any better than the low frequency roll-off allows as that is the source of the skewed phase. ... "fixed" by making the roll-off linear-phase with a phase pre-correction (DSP/FIR). Not free lunch though, and the cost is that the sequence's response now is spread out a bit farther in time, now both before (pre-ringing) and after the original sequence.
The initial question was whether the reproduction of a 60Hz square wave by a single driver is a decisive quality feature for a loudspeaker, as indicated in the initial post.
But this feature "only" means that the driver should have the most linear FR and phase frequency response possible (especially in the range above 60Hz) in order to be able to reproduce a square wave "distortion-free" - which should be achievable with any good active studio monitor.
Then I said the fateful sentence in
post#73 that triggered the whole discussion between
@Hayabusa and me:
If the phase frequency response was linearized in spring at 20°C (293K), then in summer at 30°C (303K) temperature dependence of the speed of sound leads to considerable phase shifts, so that the square wave will show significant distortion. At a distance of 5m, the phase shift would be around 11°@100Hz and around 110°@1000 Hz.
Which means when we have an ideal loudspeaker that is calibrated to a distance of 5m@20°C reproducing a square wave recorded with an mic.
What happens with the reproduction of the square wave when the temperature increases e.g. to 30°C. Will the mic in 5m distance still record a perfect square wave or will the frequency depended phase shift "distort" the square wave?
Update: This statement is wrong, phase shift occur but the square wave will not be distorted - the replies from others pointing out the error are correct.
Now comes the crucial point, if the measurement conditions are not changed (the mic and the measurement software are left completely unchanged), a phase shift occurs due to the time offset (because of the difference in the speed of sound at 20°C and 30°C) which "distorts" the plot of the square wave.
There may have been a misunderstanding between @Hayabusa and myself at this point.
Normally, the time of flight from the sound source at the driver and the microphone is cut out after the measurement. However, this is not what arrives at the ear/mic, as there is an additional phase shift due to the temperature change.
Rene pointed out this difference in his answer:
So if you measure a particular phase with c=c(f,T1,humidity1), you can measure a very different phase for another sound speed c=c2(f,T2,humidity2). This issue is not that one is more correct than the other, and so it is a bit of misnomer to say that there is a phase error. This issue is that typically you want to get rid of this phase all together, because it is trivial compared to the transducer phase, which is the interesting one, and that would typically be pressure phasor phase related back to voltage phasor phase.
Why does Klippel calls it a phase error:
A phase error can creep in during speaker design due to temperature changes.
As a rule, we do not know the exact point of sound generation in the driver (as a rule of thumb, we often take the position of the voice coil in the direction of the measurement axis). At high crossover frequencies, this can lead to large frequency response errors, as an incorrectly estimated offset of just a centimeter or so between the drivers leads to significant phase deviations.
To avoid this, a fixed time of flight (reference point) is assumed for all measurements (then the correct relative sound generation off-set between the drivers is in the measurements) - for example, the time of flight of the on-axis measurement of the tweeter (and tweeter voice coil as rotation axis for all measurements).
If measurements of the tweeter are carried out and then the measurements of the midrange driver, phase deviations between the tweeter and midrange driver may occur if the temperature of the measuring room increases, as the time of flight is a fixed value.
From this perspective, these are then temperature-related phase errors.