In the figure below are shown graphs which could represent properties of pulses

Question

In the figure below are shown graphs which could represent properties of pulses on a stretched string. For the situation and the properties (a) (e) below, select which graph provides the best representation of the given property. If none of the graphs are correct, write "none" Two pulses are started on a stretched string. At time t-to, an upward pulse is started on the right that moves to the left. At the same instant, a downward pulse is started on the left that moves to the right. At to their peaks are separated by a distance 2s. The distance between the pulses is much larger than their individual widths. The pulses move on the string with a speed vo . The scales in the graphs are arbitrary and not necessarily the same. (a) which graph best represents the appearance of the string at time t0?A -X (b) Which graph best represents the appearance of the string at a time ty+s/vo? -Seloct- (c) Which graph best represents the appearance of the string at a time to + 2s/vo? E (d) Which graph best represents the velocity of the string at a time tsv? D (e) which graph best represents the appearance of the string at a time to s/tu + where is small compared to s/vo?E

Explanation / Answer

1. The question states that at t=t0

Upward pulse -> right to left

Downward pulse-> lef to right

So Answer would be (B)

2. At t = t0 +s/v0 , the pulses will be at same spot, i.e. the center of the string, as these pulses are in opposite direction, they will destructively interefere.

hence, The ampliture will be 0

Which is shown in image D

hence, (D)

c) At t = t0 +2s/v0 , the travelling pulses will reach at the opposite ends.

The pulse which started from right will be at left and vice versa,

Hence, the image will be exact opposite of initial condition.

Answer will be (A)

d) Velocity of the string = Velocity of pulse 1 + velocity of pulse 2   (we are adding because the pulses are travelling in opposite directions, and hence relative velocity will add up)

Velocity of the string = 2v0

This is represented by Graph C

Hence, option (C)

e) After the interference,the pulses will resume travelling in their own directions, hence, (E)

To summarize :

a) B

b) D

c) A

d) C

e) E

                                 

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