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 = 23.2 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? s (c) What is the value of this maximum amplitude? cm

Explanation / Answer

Given v = 23.2 cm/s

At t = 0 pulse 1 is at x = 6 cm and pulse 2 is at 34.5 cm

Pulse 1 is travelling to right and pulse 2 is travelling to left. They cover the distance between them together ( 34.5 - 6 = 28.5 cm ) together.

They meet at time t given by

28.5 = 23.2*t +23.2*t

Therefore t = 0.614 s

The pulses meet at x = 14.25 cm

midway between 6 & 34.5 cm as the pulses cover equal distances.

a) The resultant of two pulses will have max amplitude when their peaks coincide . This happens when pulses are at x = 14.25 cm

b) The resultant of two pulses will have max amplitude when their peaks coincide . This happens at t = 0.614 s

c) Max amplitude of the resultant pulse = sum of amplitudes of the pulse

                                                         = 6 + 9 =15 cm

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