Question

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

• A. The wave is travelling to the right.
• B. Displacement amplitude of the wave is equal to the 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 $\frac{\pi }{2}$.

Answer 1

Answer: (B), (D)

The correct options are
B Displacement amplitude of the wave is equal to the displacement of $B$ at this instant.
D Phase difference between $A$ and $C$ may be equal to $\frac{\pi }{2}$.

Since $A$ is moving upwards, after an elemental time interval, the wave will be as shown dotted in the figure. It means the wave is travelling leftwards. Therefore option (a) is wrong.


Displacement amplitude of the wave means maximum possible displacement of the particles of the medium, due to propoagation of the wave which is equal to the displacement at $B$ at the instant shown in the question figure. Hence option (b) is correct.

From the question figure, it is clear that $C$ is moving downwards at this instant. Hence option (c) is wrong.

The phase difference between two points will be equal to $\frac{\pi }{2}$, if distance between them is equal to $\frac{\lambda }{4}$. Between $A$ and $C$, the distance is less than $\frac{\lambda }{2}$. It may be equal to $\frac{\lambda }{4}$. Hence the phase difference between these two points may be equal to $\frac{\pi }{2}$. Therefore, option (d) is correct.