Answered: A wave of amplitude 0.40 m interferes…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

A wave of amplitude 0.40 m interferes with a second wave of amplitude 0.26 m traveling in the same direction. (a) What is the largest resultant amplitude that can arise, and under what conditions will this maximum occur? m (b) What is the smallest resultant amplitude that can arise, and under what conditions will this minimum occur? m

Expert Solution

Step 1: Part (a)

When two waves propagating in the same direction superimposed then the amplitude of the resultant wave is given by:

A= $\sqrt{A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} \cos ϕ}$ Where $ϕ$ is the phase difference of waves

When $ϕ$ =0 then

A = $\sqrt{A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} \cos 0}$ = $\sqrt{A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2}}$ = $(A_{1} + A_{2})$ which is largest

So largest resultant amplitude occurs when the phase difference between waves is 0.

A_Largest= $(A_{1} + A_{2})$ =0.40+0.26=0.66 m

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