Half the Wavelength Explained: Identify the Correct Wave Segment with Examples

Solution for Half the Wavelength

Question

In the given curve, which segment represents half the wavelength?

Options:

  1. AB
  2. BD
  3. DE
  4. AE

Wave Diagram

A B D E

Diagram illustrating wave segments AB, BD, DE, and AE.

Solution Explanation

A single full wavelength (\(\lambda\)) is measured between two points on the wave that are in the same phase (for example, from crest to the next consecutive crest, or from zero-crossing with the same slope to the next such zero-crossing). From the diagram:

  • \(A\) and \(E\) are successive zero-crossings with the same slope, so \(AE = \lambda\).
  • \(B\) and \(D\) appear to be a crest and the next trough (or vice versa), which are separated by half a wavelength \(= \frac{\lambda}{2}\).
  • The segments \(AB\) or \(DE\) each represent a quarter wavelength \(\frac{\lambda}{4}\), because they go from a zero-crossing to an extreme (crest or trough) or from an extreme back to a zero-crossing.

Hence, the distance that corresponds to half the wavelength is BD.

Answer: (b) BD

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