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Superposition, Interference and Diffraction

Path difference and phase difference

  • 3 things to know
  • Unit AS 2

Overview

Recall questions on the definition of path difference, the whole-wavelength and half-odd-wavelength conditions for constructive and destructive interference, the same conditions in terms of phase, why the central fringe is always bright, worked examples with given path differences, and two loudspeakers wired out of phase.

What you need to know

Answer each one before you reveal it.

Your recallNot started
Key term

State the condition on path difference for constructive interference.

Key term

State the condition on path difference for destructive interference.

Key term

State the conditions for constructive and destructive interference in terms of phase difference.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    Define path difference.

    Model answer

    The path difference at a point is the difference between the distances travelled from each of the two sources to that point, measured in metres.

  2. 2

    State the condition on path difference for constructive interference.

    Model answer

    Constructive interference occurs where the path difference is a whole number of wavelengths, that is nλ where n is 0, 1, 2, and so on.

  3. 3

    State the condition on path difference for destructive interference.

    Model answer

    Destructive interference occurs where the path difference is an odd number of half wavelengths, that is (n + ½)λ.

  4. 4

    State the conditions for constructive and destructive interference in terms of phase difference.

    Model answer

    Constructive interference occurs when the phase difference is a whole number of full cycles, that is 2πn radians, and destructive interference when it is an odd multiple of π radians.

  5. 5

    Waves from two coherent sources arrive at a point with a path difference of 1.5 wavelengths. What is observed there?

    Model answer

    The point is dark or quiet, because an odd number of half wavelengths means the waves arrive in antiphase and cancel.

  6. 6

    Waves from two coherent sources arrive at a point with a path difference of exactly two wavelengths. What is observed there?

    Model answer

    The point is bright or loud, because a whole number of wavelengths means the waves arrive in phase and reinforce.

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