EBK PRECALCULUS W/LIMITS
EBK PRECALCULUS W/LIMITS
3rd Edition
ISBN: 9781285607160
Author: Larson
Publisher: CENGAGE CO
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Chapter 5.4, Problem 80E
To determine

To prove: The addition of two wave is y1+y2=2Acos2πtTcos2πxλ .

Expert Solution & Answer
Check Mark

Explanation of Solution

Given:The equations of a standing wave is obtained by adding the displacement of two waves travelling in opposite directions as shown in figure. Assume that each of the waves has amplitude A , period T, and wavelength λ . If models for these waves are

  y1=Acos2π(tT−xλ) and y2=Acos2π(tT+xλ)

  EBK PRECALCULUS W/LIMITS, Chapter 5.4, Problem 80E

The models of two waves are y1=Acos2π(tT−xλ) and y2=Acos2π(tT+xλ) .

Now add both waves and simplify the equation.

Therefore,

  y1+y2=Acos2π(tT−xλ) +Acos2π(tT+xλ)=A[2cos(2π(tT−xλ)+2π(tT+xλ)2)cos(2π(tT−xλ)−2π(tT+xλ)2)]=2Acos2π(2tT2)cos2π(2xλ2)=2Acos2π(tT)cos2π(xλ)

Hence proved

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Chapter 5.4, Problem 79E
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Chapter 5.4, Problem 81E

Chapter 5 Solutions

EBK PRECALCULUS W/LIMITS

Ch. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Prob. 6ECh. 5.1 - Prob. 7ECh. 5.1 - Prob. 8ECh. 5.1 - Prob. 9ECh. 5.1 - Prob. 10E
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