At t = 0, the instantaneous position of two pulses moving along a taut string wi

Question

At t = 0, the instantaneous position of two pulses moving along a taut string with a speed v = 24.9 cm/s are as shown in the diagram below. Each unit on the horizontal axis is 3.0 cm and each unit on the vertical axis is 3.0 cm. (The peak of pulse 2 is exactly on a half unit of the horizontal axis.)

(a) At what location will the resultant of the two pulses have maximum amplitude?

(b) At what time will the resultant of the two pulses have maximum amplitude?

(c) What is the value of this maximum amplitude?

Explanation / Answer

a)

The distance between the maxima of the two waves is:

d = 9.5 unit = 9.5 * (0.03) = 0.285 m

The maximum of the waves will arrive together at the middle of d:

x = 0.06 + d/2 = 0.06 + 0.285/2 = 0.2025 m = 0.20 m = 20 cm

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b)

t = d/(2 v) = (0.285)/(2*(0.249)) = 0.57 s

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c)

Amax = A1max + A2 max = 0.06 + 0.09 = 0.15 m = 15 cm

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