phase and time

[Coda II]

This question cropped up elsewhere:

Can we assume a 'perfect' pair of speakers being fed 'perfect' test tones and reproducing them perfectly such that what we hear is just pure single tones.

If we play a mono 100 Hz signal through both speakers and listen at the prefect sweetspot in our perfect room we should hear a tone from midway between the speakers shouldn't we.

If we then introduce a delay to the tone to one of the speakers of 1/200th of a second (ie half the period of the tone) would the speakers relative to the listener now be 180 degrees out of phase?

Assuming the answer to that is yes, we move on

Keeping the delay of 1/200th sec we move to a tone of 50Hz, the time delay is now one quarter the period of our tone so are the speakers now out of phase by 90 degrees?

Then again we move to a tone of 200 Hz but still keep the 1/200th delay; the delay is now equal to the period so are we now 360 degrees out of phase and in this particular (artificial) instance does that mean that they are effectively back in phase?

Lastly, we remove our time delay and instead we reverse the polarity (black for red) on the back of one of our speakers and the replay each of our tones - 50 Hz, 100 Hz, 200 Hz separately, what is the effect on the phase of each of these tones (relative to the perfect listener) now?

Phase is one of those hifi things that crops up a fair bit, seems straightforward, but I for one have never really understood it.

I don't know the answers to the questions above and given (as is often the way in forum land) interest seems to have faded in the particular thread in which they appeared I also don't know if they are just daft questions or simply ones that no one can quite be bothered to answer.

 

[Tenson]

I think the issue with the quoted comments is a confusion in the words. A time delay produces a 'phase shift' which can be represented as a number of degrees. You can have a phase shift of more than 360-degrees.

'Out of phase' and 'In phase' is just relative to the two signals. You could have a 360-degree phase shift, and the two signals would be 'in phase' with each other, but also still phase shifted, or delayed.

Polarity is just when you change the connections on the speaker or other equipment. There is no delay, but when one device moves positive, the other moved negative. This makes them 180-degrees 'out of phase' relative to each other, but there is no phase shift or delay.

It gets more complicated when you start to consider the wider effects of time domain on speakers...