Transverse waves on a string have wave speed 8.00 m/s, amplitude 0.0700 m, and w

Question

Transverse waves on a string have wave speed 8.00 m/s, amplitude 0.0700 m, and wavelength 0.320 m. These waves travel in the x  direction, and at t = 0 the x = 0 end of the string is at y = 0 and moving downward.

a) Find the frequency of these waves. (Found it to be 25 Hz)

b) Find the period of these waves. (Found it to be 4.00x10-2 s)

c) Write the equation for y(x,t) describing these waves. (Found this to be y = .07sin(19.6x-157t) )

d) Find the transverse displacement of a point on the string at x2 = 0.120m at time t2 = 0.105s . (This is the one I'm having trouble with)

Explanation / Answer

Equation of the wave is y = 0.07 sin(19.6x - 157t). 'y' represents the vertical displacement, x is the position at which displacement is to be calcualted and 't' is time. Substituting x = 0.120 m and t = 0.105, phase of the displacement 19.6x - 157t = 19.6 x 0.120 - 157 x 0.105 = 2.352 - 16.485 = -14.133 = - 4.5 pi. Then, y = 0.07 sin(-4.5 pi) = -0.07. As sin (-x) = - sin x and 4.5 pi = (4 + 1/2) pi. Then sin (4 + 1/2) pi = sin(pi/2) = 1.

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