Two microwaves with different frequencies have the same phase at regular intervals, the interval is 1/(the difference between the frequencies). It is nearly like asking "If two trains with different window spacing are travelling beside each other, are the windows opposite each other?" The answer is sometimes, in some places, but never all at once.
1. Recall that angular frequency is the change in phase with time. For example, a 1000Hz signal undergoes a phase change of 2(pi) *1000 radians per second. The starting phase of the signal is somewhat arbitrary.
2. If you plot phase (radians) versus time on a graph, the result is a straight line with slope equal to the angular frequency.
3. Lets start two microwave signals with different frequencies at "zero phase" on the plots, at t=0 seconds. We then have 2 straight lines starting at (0,0) and having different slopes. Therefore they never cross, or possess the same phase mathematically.
However, if you wrap the phase such that 0 = 2(pi)=4(pi) ..., then you could say that 2 different frequencies are at the same phase at periodic time intervals.
For example, a signal and its harmonics will be at the same phase periodically along the time access. You can observe this by plotting 1000Hz and 2000Hz both starting at 0 phase at t=0.
Thank all your answers, and espically the Malcolm White and Peter Nanni' . I think I got.
Then a query come into my brain:The phase in classical physics means the coherence in quantum physics? if two laser (or microwave) has the same phase (such as 0, 2pi, 4pi,...) at some special times for a chosen space, does it mean that they are "coherence” on these times ? Take another sentence, only on these times, they "appear" at the same time.
For any pair of signals at any frequency there will usually be places and times where they have the same phase, but this does not count as coherence. Two signals can also have different phases that change over time and still be coherent. This is the case with coherent radar receivers - the received signal is coherent with the radar reference but changes over time. Because they are coherent the changing difference in phase gives information about the range and velocity of the target.
Coherency usually means that a mathematical relationship exists between the phases of the two signals, that could be used to get information about how one of them has changed.