e represented by Eql 2. (II) Suppose two linear waves of equal amplitude and frequency have a phase difference o as they travel in the same medium. They can be represented by D = A sin(kx – wt) %3D D = A sin(kx – wt + ). bns 1oisllineo %3D sin 01 + sin 02 = (a) Use the trigonometric identity 2 sin (0, + 02) cos (0, – 02) to show that the resultant wave is given by %3D CoS (24 o sin kx- 2) D = (2A cos wt + %3D (b) What is the amplitude of this resultant wave? Is the wave purely sinusoidal, or not? (c) Show that constructive interfer- ence occurs if = 0, 2, 4T, and so on, and destructive interference occurs if o = T, 3T, 5T, etc. (d) Describe the resultant wave, by equation and in words, if o = T/2. %3D %3D

e represented by Eql 2. (II) Suppose two linear waves of equal amplitude and frequency have a phase difference o as they travel in the same medium. They can be represented by D = A sin(kx – wt) %3D D = A sin(kx – wt + ). bns 1oisllineo %3D sin 01 + sin 02 = (a) Use the trigonometric identity 2 sin (0, + 02) cos (0, – 02) to show that the resultant wave is given by %3D CoS (24 o sin kx- 2) D = (2A cos wt + %3D (b) What is the amplitude of this resultant wave? Is the wave purely sinusoidal, or not? (c) Show that constructive interfer- ence occurs if = 0, 2, 4T, and so on, and destructive interference occurs if o = T, 3T, 5T, etc. (d) Describe the resultant wave, by equation and in words, if o = T/2. %3D %3D

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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Concept explainers

Interference of sound

Seiche

A seiche is an oscillating standing wave in a body of water. The term seiche pronounced saysh) can be understood by the sloshing of water back and forth in a swimming pool. The same phenomenon happens on a much larger scale in vast bodies of water including bays and lakes. A seizure can happen in any enclosed or semi-enclosed body of water.

Question

e represented by Eql
2. (II) Suppose two linear waves of equal amplitude and
frequency have a phase difference o as they travel in the
same medium. They can be represented by
D = A sin(kx – wt)
%3D
D = A sin(kx – wt + ). bns 1oisllineo
%3D
sin 01 + sin 02 =
(a) Use the trigonometric identity
2 sin (0, + 02) cos (0, – 02) to show that the resultant
wave is given by
%3D
CoS
(24
o sin kx- 2)
D = (2A
cos
wt +
%3D
(b) What is the amplitude of this resultant wave? Is the wave
purely sinusoidal, or not? (c) Show that constructive interfer-
ence occurs if = 0, 2, 4T, and so on, and destructive
interference occurs if o = T, 3T, 5T, etc. (d) Describe the
resultant wave, by equation and in words, if o = T/2.
%3D
%3D

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