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, sExplanation / 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
----------------------
(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
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