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The wave from S1 has to travel 100cm. Using Pythagoras theorem, S2 will have to travel 128.1 cm.There is a path difference of 28.1 cmB Part, in detail please, explain any formulas used :/
Using v =f lambda, we know that
lambda= 330/1000 to 330/4000 Thus
8.25cm <= lambda <= 33 cm
Now, we know that a minima is formed when S2 is at its trough, while S1 at its crest. As both waves have the same frequencies, they will have travelled the same amount of distance in their respective first 100cm. However, in the next 28.1 cm, S2 must have travelled at least half, 1.5, 2.5 and so on cycles to cause destructive interference and thus a minima. We will check this with different possible wavelengths.
28.1 = 0.5 lamda
lamda = 56 cm. This is outside our range
28.1 = 1.5 lamda
lamda = 18.73. This is in our range
28.1 = 2.5 lamda
lamda = 11.24 cm This is in our range
28.1/3.5 = 8.02 Outside our range
answer = 2