Consider the following list: i) single slit diffraction of sound waves ii) 2-sli

Question

Consider the following list:
i) single slit diffraction of sound waves
ii) 2-slit interference of small amplitude water waves
iii) beats from a pair of tuning forks
iv) the expression for the general solution to the 1-dimensional wave equation
v) the Doppler shift
vi) 2-slit interference for electrons

a) Which of the above does does not involve the superposition principle? (Explain)

b) Consider (ii) and (vi). Explain qualitatively the basic physics of how the superposition principle leads, in both cases, to the interference pattern.

c) Yet there is an important difference. Describe the quantities to which the superposition is applied in the two cases (ii) and (vi). In what way are these quantities fundamentally different?

Explanation / Answer

a) the expression for the general solution to the 1-dimensional wave equation does not involve the super position principle. For the super position principle to apply minimum two waves are required. b) Interference means the distribution of the energy . When crest of one wave superposes with the crest of one wave then constructive interference takes place and when crest of one wave superposes with the trough of one wave then destructive interference takes place. c) For water waves displacement is super imposed where as in electron beams , intensity is superimposed. And intensity is directly proportional to the square of the amplitude.

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