Name: Standing Waves
Uploaded: 2019-07-19
Duration: 8 min 34 s
Description: Have you ever played the guitar? How does putting fingers on the string change the frequency of the sound produced? Curious? Watch the video and unravel the...

Question

The wave pulses shown in the diagram travel at $1 cm s^{- 1}$ and both have width $2 cm$ . The heights are indicated on the diagram. In each case, draw the shape of the resulting pulse according to the principle of superposition at times $t = 0.5 s$ , $t = 1.0 s$ and $t = 1.5 s$ . Take $t = 0 s$ to be the time when the pulses are about to meet each other.

Accepted Answer

Using the principle of superposition we will overlap the positive and negative pulse at different period:

At $t = 0 s$ :

The point where positive pulse ends the negative pulse starts from there.

At $t = 0.5 s$ :

Here after $1 cm$ of positive pulse of $+ 1 unit$ height, the height of the pulse is $- 1 unit$ for $1 cm$ and then the pulse of height $- 2 unit$ for $1 cm$ .

At $t = 1.0 s$ :

Here, the positive pulse and negative pulse will completely overlap and the resultant pulse will be $- 1 unit$ .

At $t = 1.5 s$ :

Here, the negative pulse will come of height $2 units$ for $1 cm$ then overlapping of positive pulse on negative pulse making the pusle height $- 1 unit$ for $1 cm$ and the next pulse is completely positive with height $1 unit$ for $1 cm$ .

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