when two wave sources are in-phase, and the wave from one source has to travel one-half wavelength further from the wave from the other source, there will be
a. destructive interference
b. constructive interference
c. alternating constructive and destructive interference
d. simultaneous constructive nor destructive interference
e. no interaction
b. constructive interference
a.
Destructive interference occurs when two wave sources are out of phase and the peaks of one wave line up with the troughs of the other, resulting in the waves cancelling each other out. When two wave sources are in phase, the peaks and troughs of the waves line up, resulting in constructive interference where the amplitude of the resulting wave is greater than either individual wave.
So if they are half a wavelength out of phase?
If two wave sources are half a wavelength out of phase, then the peak of one wave will line up with the trough of the other and vice versa. This will result in destructive interference where the waves cancel each other out.
However, if the two wave sources are in-phase and the wave from one source has to travel half a wavelength further than the wave from the other source, they will still interfere constructively. This is because the peaks and troughs of the waves will still line up, resulting in an increased amplitude of the resulting wave.
I think we are looking at two slit diffraction where they hit the panel in phase but have a minimum at an angle when one travels half a wavelength further.
Ah, I see what you're referring to now. Yes, in the case of two-slit diffraction where one wave has to travel half a wavelength further than the other wave to reach a point on the screen, there will be a minimum of intensity at that point due to destructive interference.
This is due to the fact that the waves from the two slits arrive out of phase at that point, with the crest of one wave meeting the trough of the other wave. This results in destructive interference and a minimum of intensity at that point on the screen.
However, in general, when two wave sources are in-phase, they will interfere constructively as the crests of one wave will meet with the crests of the other wave resulting in an increase in amplitude of the resulting wave