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  • The displacement of an elastic wave is given by the function y = 3 sin ωt + 4 cos ωt where y is in cm and t is in second. Calculate the resultant amplitude.

The displacement of an elastic wave is given by the function y = 3 \sin \omega t + 4 \cos \omega t where y is in cm and t is in second. Calculate the resultant amplitude.

Answers (1)

y=3 \sin\omega t+4\cos \omega t

Let 3=a\cos\phi and 4=a \sin\phi ;

\tan\phi =\frac{4}{3} or \phi = tan^{-1}\frac{4}{3}

a^{2}(\cos\phi )^{2}+a^{2}(\sin\phi) ^{2}=3^{2}+4^{2}

a^{2}(\cos^{2}\phi +\sin^{2}\phi )=9+16

a^{2} = 25

a=5

 Now, y=a\cos\phi \sin \omega t+a\sin\phi \cos\omega t

y=a \sin (\omega t+\phi) 
 y=5\sin (\omega t+\phi) where

\phi = tan^{-1}\frac{4}{3}

Posted by

infoexpert24

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