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Can someone plz plz plz explain this question to me... I would really be grateful
Taking a look at the image and the details we are given, it seems to be too cumbersome to count the waves at each point and check if they are 1/8th out of phase. In fact, determining what 1/8th out of phase is would be a big headache. So, let's turn to mathematics and try to form a "phase/wave equation".
(Note - there is a real wave equation that, interestingly, applies to any wave in nature. It is a differential equation, and you do not need it for your exams, but in case you want to put this term in Google, you might not get any of the answers you are looking for)..
Okay, back to the question.
We can see for both waves that each one has a constant frequency. This is very important, because otherwise we wouldn't be able to write down a simple equation to relate the wave phases. Keeping this in mind, let's proceed.
For waveform P, we note that there are 4 wavelengths in 18 seconds. This means that 1 wavelength passes by in 18/4 = 9/2 = 4.5 seconds.
So, taking this line of reasoning further, suppose we have a time "t" in mind. How do we find out how many wavelengths have occurred in this time t?
The answer is rather simple - the number of wavelengths that have passed in time t = t/4.5 . To test this, let us put t = 18 seconds. We get, as expected, the number of wavelengths that have passed in 18 seconds = 18/4.5 = 4. Good!
Repeating this procedure for the other wave, we see that the number of wavelengths of waveform Q that pass in the same "t" seconds are t/4 wavelengths.
So when the difference between these two is 1/8 of a wavelength, then we have our answer!
We can say that the second waveform completes it's waves faster than the first waveform (it has a higher frequency) so we write
t/4 = t/4.5 + (1/8)
Rearranging, t(0.25 - 0.222) = 0.125
0.0277 * t = 0.125
t = 4.5 seconds = B.