Actually, one wave and its 180 flip phase image can be seen as two waves with the same phase but with opposite amplitude (when one is positive the other is negative).
The reason you cannot hear the difference between the two is that your ear (or microphone) is not sensitive to the amplitude but rather to the intensity of the wave, i.e. the square of the absolute value of the amplitude. As you can see, the difference in amplitude sign (or the phase) does not matter and both the original and its 180 flip phase image will sound the same.
What you would like to measure to see the difference between the two is the phase of the waves but as mentioned earlier, you cannot detect the phase directly. However you can measure the interference between the waves : when waves are emitted simulatenously they sum up. Now if the two waves have the same phase, then the amplitude add up (constructive interference). If the phases are 180 degree apart, then the amplitudes will cancel out (destructive interference, mentioned above). If the phase difference is somewhere inbetween, then you will get something ... inbetween (an interference pattern).