Question

If you start with two sinusoidal waves of the same amplitude traveling in phase on a string and then somehow phase-shift one of them by 5.4 wavelengths, what type of interference will occur on the string?

Please answer with relevant math and work :)

Answer 1

Given: The phase shift is 5.4 wavelengths.

Two waves with the same wavelength are in phase if there phase difference is= 0, or an integral multiple of wavelength.

Thus the integer part of any difference expressed in wavelength can be discarded.

Since the phase shift is 5.4, this means that the peak of the shifted sine wave will be 0.4 wavelengths ahead of the non shifted sine. Fully destructive would be 0.5 wavelengths shifted, as Fully destructive interference between two sinusoidal waves of the same frequency and amplitude occurs only if they travel in the same direction and are 180° out of phase.

And, 0.4 is Intermediate closer to fully destructive.