First slide

Travelling wave

Question

A wave is travelling along a string. At an instant, shape of the string is as shown in fig. At this instant, point A is moving upwards. Which of the following statements is/are correct

Difficult

A

The wave is travelling to the right
B

Displacement amplitude of the wave is equal to displacement of B at this instant
C

At this instant velocity of C is also directed upwards
D

Phase difference between A and C may be equal to $\frac{π}{2}$

Solution

Since A is moving upwards, therefore, after an elemental time interval the wave will be as shown dotted in following fig. It means, the wave is travelling leftward. Therefore, (1) is wrong.

Displacement amplitude of the wave means maximum possible displacement of medium particles due to propagation of the wave, which is equal to the displacement at B at the instant shown in fig. Hence (2) is correct.
From figure, it is clear that C is moving downwards at this instant. Hence (3) is wrong.
The phase difference between two points will be equal to $\frac{π}{2}$ if distance between them is equal to $\frac{λ}{4}$ Between A and C, the distance is less than $\frac{λ}{2}$ It may be equal to $\frac{λ}{4}$ . Hence, phase difference between these two points may be equal to $\frac{π}{2}$ .

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