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A phase difference of \pi/3 radians equivalent to a path difference of: a) six wavelengths b)...

Question:

A phase difference of {eq}\pi/3 {/eq} radians equivalent to a path difference of:

a) six wavelengths

b) three wavelengths

c) one-third of a wavelength

d) one-sixth of a wavelength

Path Difference:

The waves are characterized by their wavelength. When two waves interfere, they may give constructive or destructive interference depending on the path difference between them. A path length of one wavelength represents a phase of {eq}2\pi{/eq} radians.

Answer and Explanation:

Finding the path difference ({eq}\Delta x{/eq}) for a phase difference of {eq}\phi\ = \pi/3\ radians{/eq}

For a wave:

  • {eq}2\pi\ radians {/eq} represents one wavelength i.e.{eq}\lambda{/eq}
  • Therefore, the path difference corresponding to phase difference of {eq}\phi\ = \pi/3\ radians{/eq} is calculated as:
    {eq}\Delta x\ = \dfrac{\lambda}{2\pi}\times \phi\\\Delta x\ = \dfrac{\lambda}{2\pi}\times \pi/3\\\Delta x\ = \dfrac{\lambda}{6}{/eq}

Correct option is (d)


Learn more about this topic:

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Constructive and Destructive Interference

from CLEP Natural Sciences: Study Guide & Test Prep

Chapter 8 / Lesson 16
122K

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