Question

Which of the following is/are correct for a standing wave (wavelength is $\lambda$), created on a string fixed at both ends?

• A. The maximum distance between two consecutive particles having same amplitude is less than $\lambda$ .
  
• B. The nearby points on both sides of a node are always in opposite phase in their SHM.
  
• C. The nearby points on both sides of an antinode are always in phase in their SHM.
  
• D. The amplitude of a particle at a distance $\frac{5\lambda }{4}$ from one end is zero.

Answer 1

Answer: (A), (B), (C)

The correct options are
A The maximum distance between two consecutive particles having same amplitude is less than $\lambda$ .

B The nearby points on both sides of a node are always in opposite phase in their SHM.

C The nearby points on both sides of an antinode are always in phase in their SHM.


1. Wavelength is defined as the minimum distance between two points oscillating in the same phase with the same amplitude. For a standing wave, the wavelength is lesser than the wavelength of its constituent travelling waves.

2. A node in a standing wave is a point which has zero displacement at all given time periods. On both sides of it, points move in opposite directions in phase.

3. An antinode in a standing wave is a point which reaches maximum amplitude at perfectly placed time periods. On both sides of it, points move in same directions in phase.