Phase difference between the two waves

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For two sine waves with equal peak-to-peak amplitudes of 89 and a phase difference of 180 degrees, the resultant wave's peak-to-peak amplitude is 0 due to complete cancellation. In the case of two sine waves with equal peak-to-peak amplitudes of 81 and a phase difference of 90 degrees, the resultant amplitude is approximately 81, as they combine to form a wave with a maximum amplitude. Additionally, when light travels from point O to point X via two different paths, the phase difference at X can be calculated using the path length difference and the wavelength of 660 nm. The path length difference of 1.65 mm results in a phase difference of approximately 1.57 radians. Understanding these principles is essential for analyzing wave interactions and their resultant effects.
Sloan650
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1) Two sine waves have equal peak to peak amplitudes 89 but are out of phase by 180 degrees. What is the peak to peak amplitude of the resultant wave.

2)Two sine waves have equal peak to peak amplitudes 81 but are out of phase by 90 degrees. What is the peak to peak amplitude of the resultant wave.

3) Light from a single source goes from O to X via two paths: directly OX, path length 10.29600 mm and indirectly OYX, path length 10.29765 mm. The wavelength is 660 nm. What is the phase difference between the two waves when they meet at X.
 
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