The next time the string will have the same appearance that it did at t=0s is 2.29 s.
v = fλ
f = v/λ
where;
half of the upward pulse is a quarter of wavelength = ¹/₄ x 4 m = 1 m
f = 3.5/1
f = 3.5 Hz
t1 = 4/3.5 = 1.143 s
The next time the string will have the same appearance that it did at t=0s.
d = 4 m x 2 = 8 m
t2 = 8/3.5
t2 = 2.29 s
Thus, the next time the string will have the same appearance that it did at t=0s is 2.29 s.
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