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Question

Transverse waves of amplitude 0.05m are generated at one end of a long string (x=0). At a certain instant of time the displacement of particle A at x=1 m is 5 cm and of particle B at x=2m is +5 cm. What is the wavelength of waves?

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Solution

Amplitude =0.05m=5m
Points A & B can be
Point A is a trough & Point B is a rest, as shown in figure
As, it isn't given whether A & B are consecutive rests and troughs
d(A.B)=(n+12)λ ........(i)
Distance between a crest & a trough
where n=0,1,2,.....
Given distance between A & B=1m
From (i)
(n+12)λ=1
λ=1(n+12)m
n=0,1,2,....
For the simplest case: n=0 adjacent rest & trough.
λ=2m.

1182657_705624_ans_df1a8d1cfa6e458ca8b13cf3f5d14cce.jpeg

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