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10 minutes. A wave is traveling with a speed v along a taut string. We wil call

ID: 1651879 • Letter: 1

Question

10 minutes. A wave is traveling with a speed v along a taut string. We wil call the direction of propagation the + x axis. The upper graph shows the displacement of the string y versus the position x for a given instant of timet. The lower graph shows the displacement y versus the time for any given point t. (a) From the information in the graphs, calculate the wave speed v. (b) If the amplitude of the wave is A 2.0 meters, calculate the maximum speed of the simple harmonic motion that created the wave in the taut string. 1.rn im t, s

Explanation / Answer

(A) lambda = 4 m

T = 0.5 sec

v = lambda / T = 4 / 0.5

v = 8 m/s

(B) w = 2pi / T = 12.6 rad/s

v_max = A w = 12.6 x 2 = 25.2 m/s

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(A) ME = k A^2 /2

0.90 = (2000) A^2 / 2

A = 0.03 m Or 3 cm

(B) 0.90 = 5 v^2 /2

v = 0.6 m/s

(C) w = sqrt(k/ m) = sqrt(2000 / 5) = 20 rad/s

x = 3 cm sin(20t)


(d) 0.026 = 0.03 sin(20t)

t = 0.052 sec