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  4. The equations of two waves are given by: y1=5 sin 2 π(x-v t) cm y2=3 sin 2 π(x-v t+1.5) cm These waves are simultaneously passing through a string. The amplitude of the resulting wave is

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Q. The equations of two waves are given by:
$y_{1}=5 \sin 2 \pi(x-v t) cm$
$y_{2}=3 \sin 2 \pi(x-v t+1.5) cm$
These waves are simultaneously passing through a string. The amplitude of the resulting wave is

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Solution:

$A _{1}=5 \,\,\,A _{2}=3$
$\Delta \theta=2 \pi(1.5)=3 \pi$
$A _{\text {net }}=\sqrt{ A _{1}^{2}+ A _{2}^{2}+2 A _{1} A _{2} \cos (3 \pi)}$
$=\left| A _{1}- A _{2}\right|$
$=2 \,cm$