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

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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