What is fundamental difference between wave and its 180 flip phase? I'm studying property of sound wave and I was wondering what is difference between two waves (one is original and one is 180 flip phase of original) ?
Amplitude and frequency remains same and also wavelength is same, so are they same?? I could not detect any difference from hearing two sounds. If different what is different and can human/computer detect it? What is basically difference between two waves?
 A: 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).
A: If you play them simultaneously then they will destructively interfere provided they arrive at the listener at the same time (no additional phase difference). This is the basis of noise cancellation.
A: The difference is that at each instant in time, the 180-degree delayed wave has exactly the opposite value of the original wave. 
If $y_1(t) = \sin(2\pi{}ft)$ and $y_2(t) = \sin(2\pi{}ft + 180^\circ)$, then $y_1(t)=-y_2(t)$ for all t.
If you are talking about a sound wave, then whenever one wave has a minimum of pressure, the other has a maximum and vice versa.
As other answers said, this difference is not perceptible to human hearing because the ear is not sensitive to phase differences or delays on the scale of a single cycle of a sound wave.
