A transverse wave on a string is described by the followingequation. y ( x, t )

Question

A transverse wave on a string is described by the followingequation. y(x, t) = (0.35 m) sin[(1.25rad/m)x + (114.0rad/s)t] Consider the element of the string at x = 0. (a) What is the time interval between the firsttwo instants when this element has a position of y =0.175 m?
1 ms

(b) What distance does the wave travel during this timeinterval?
2 m y(x, t) = (0.35 m) sin[(1.25rad/m)x + (114.0rad/s)t] (a) What is the time interval between the firsttwo instants when this element has a position of y =0.175 m?
1 ms

(b) What distance does the wave travel during this timeinterval?
2 m

Explanation / Answer

y = A sin k (x - v t) represents a wave traveling in the + xdirection    and k = 2 / So 1.25 x + 114 t = 1.25 (x + 91.2 t) v = -91.2 m / s       the waveis traveling to the left = 2 / k = 5.03 m The distance between successive displacements of .175 m is t = / v = 5.03 / 91.2 = .055 sec As a check if take the point y = 0 at t = 0 then y shouldagain be zero in .055 sec and x = -5.03 m -1.25 * 5.03 + 114 * .055 ˜ 0  

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