A traveling wave propagating on a string is described by the following equation:

Question

A traveling wave propagating on a string is described by the following equation:
y(x, t) = (4 mm)

sin(166.87 m-1)x - (322.94 s-1)t + 0.7854

.
(a) Determine the minimum separation,
?xmin,
between two points on the string that oscillate in perfect opposition of phases (move in opposite directions at all times).


(b) Determine the separation,
?xAB,
between two points A and B on the string, if point B oscillates with a phase difference of 0.7854 rad compared to point A.


(c) Find the number of crests of the wave that pass through point A in a time interval ?t = 12 s and the number of troughs that pass through point B in the same interval.


(d) At what point along its trajectory should a linear driver connected to one end of the string at x = 0 start its oscillation to generate this sinusoidal traveling wave on the string?

Explanation / Answer

a) its lamda . 2pi/lamda=166.87 so lamda=0.038(m). b) difference in phases. so we have 166.87*(x1-x2)=0.7854 so (x1-x2)=4.7e-3(m). c)in 12s, number of oscillations. N=12*322.94/2pi=616. so there are 616 crests and 616 trough. d) dont understand the prob

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