Question

The path difference, time difference and phase difference between two successive zones will be:
A. ${\displaystyle \frac{\lambda }{2}},{\displaystyle \frac{T}{2}}$ and $\pi$
B. $\lambda ,T$ and $\pi$
C. ${\displaystyle \frac{\lambda }{2}},{\displaystyle \frac{T}{2}}$ and ${\displaystyle \frac{\pi }{2}}$
D. ${\displaystyle \frac{\lambda }{2}},{\displaystyle \frac{T}{2}}$ and $2\pi$

Answer 1

Hint:
First let us see what path difference, time difference and phase difference means-
The distance travelled by the two waves from their respective node to an antinode in the pattern is the path difference.
The time period in which waves travel between a node and antinode is the time difference.
When two or more alternating quantities approach their limit or zero values, then phase difference is used to define the difference in degrees or radians.

Complete step by step solution:
An alternating sequence of nodes and antinodes is often a standing wave sequence. The points considered to shape stationary waves are nodes and antinodes.
The distance between the two successive nodes can be calculated by considering the locations where a node and an antinode are created within a medium in a wave. The nodes are created at unique locations where destructive interference takes place. Antinodes are the points that often vibrate between the points of large positive and large negative displacement between each other.
Stationary waves are produced by nodes and antinodes.
The difference between any two successive nodes or any two successive antinodes in a given stationary wave is always half the wavelength.
Similarly, the time difference is also half the time period between two successive zones.
The phase difference will be ${180}^{\circ }$ between two successive zones.
So, the phase difference, path difference and time difference between two successive zones are $\pi ,{\displaystyle \frac{\lambda }{2}}$ and ${\displaystyle \frac{T}{2}}$ respectively.
Hence, option A is correct.

Note:
Here we should not be confused between crests, troughs; nodes and antinodes. A transverse wave consists of crests and troughs but a stationary wave consists of nodes and antinodes.