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Question

The amplitude of a wave represented by the displacement equation y=1asinωt±1bcosωt will be

A
a+bab
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B
a+bab
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C
a±bab
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D
a+bab
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Solution

The correct option is D a+bab
Given ,
y=1asinωt±1bcosωt
We can re write the above equation as,
y=1asinωt±1bsin(π2+ωt)
This is a superposition of two waves, having phase difference ϕ=π2

Resultant amplitude
R=(A)2+(B)2+2ABcosϕ

R= (1a)2+(1b)2+2π1a×1bcos90
R=1a+1b=a+bab
Thus, option (d) is the correct answer.

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