When two signals are out of phase, their waveforms have a relative phase shift or a phase difference between them. The phase difference is typically measured in degrees or radians and represents the displacement between the peaks or zero crossings of the two signals.
Let's consider a given signal with a specific wavelength and amplitude. If we have another signal with the same amplitude but a wavelength that is 180° out of phase with the given signal, it means that the peaks of one signal align with the troughs of the other signal, and vice versa. When these two signals are combined, they will interfere with each other, resulting in destructive interference. In other words, the peaks of one signal cancel out the troughs of the other signal, leading to a reduced overall amplitude or complete cancellation if the signals have equal magnitudes.
Now, if we compare this scenario with a signal that is 540° out of phase with the given signal, it corresponds to a phase difference of one and a half cycles or three half-wavelengths. In this case, the two signals will have their peaks aligned again, and their troughs will also align. Therefore, when combined, these signals will interfere constructively. The peaks reinforce each other, and the troughs reinforce each other as well, resulting in an increased overall amplitude.
To summarize, when a given signal and a signal 180° out of phase are combined, they exhibit destructive interference, leading to a reduced overall amplitude or cancellation. On the other hand, when a signal is 540° out of phase, it corresponds to a phase difference of three half-wavelengths and results in constructive interference, causing an increased overall amplitude.