# 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?

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.

• I know the fact that the other sound wave has opposite value of original wave. Maybe I did not state it clearly.. so you are saying human can hear same sound and not be able to detect difference right? By all mean, they are same sound in general? – REALFREE Nov 15 '13 at 19:19
• Yes, the human ear would hear the same thing in each case. You could also think of the "flipped" wave as being delayed by 1/2 of a cycle, something on the order of 0.05 to 10 milliseconds. The human ear is not sensitive to delays of that scale. – The Photon Nov 15 '13 at 19:46

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).

• What you are saying is that two wave with opposite amplitude are same?? I believe amplitude doesn't have sigh its just absolute value of power of wave at that point. – REALFREE Nov 15 '13 at 2:00
• Amplitude does have a sign and flipping a waveform 180 degrees also runs the waveform in reverse. – Brandon Enright Nov 15 '13 at 2:08
• @BrandonEnright ok I was wrong, then could you please tell me what's difference between - + amplitude? – REALFREE Nov 15 '13 at 3:06
• The "difference between - + amplitude" is the observer's (or other wave's) position in time. at a given time t=0 the amplitude is positive, when time moves so that the sine function goes 180 degrees the amplitude becomes negative. – anna v Nov 15 '13 at 7:32
• @annav so in fact they are same wave but playing at different position in time? Let's say I play original sound at x = 0, and play 180 flip phase sound at x = 5 (let's just assume distance 5 is wavelength) then would computer recognize them as same wave? – REALFREE Nov 15 '13 at 19:40

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.

• I know if I play simultaneously they will cancel each other. My question was what is difference between those two waves? – REALFREE Nov 15 '13 at 1:59
• A 180 degree rotation of the waveform won't cancel. A mirror about the amplitude axis (invert the amplitude) will. A 180 degree rotation of the waveform runs the original waveform in reverse with the inverse amplitude. – Brandon Enright Nov 15 '13 at 2:17
• That was what I meant tho.. well maybe it was not the same thing. – REALFREE Nov 15 '13 at 3:08