Question
In the given curve, which segment represents half the wavelength?
Options:
- AB
- BD
- DE
- AE
Wave Diagram
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