Two waves represented by $ y_{1}= $ $ 10 \sin (2000 \pi t) $ and $ y_{2}= $ $ 10 \sin (2000 \pi t+\pi / 2) $ are superimposed at any point at a particular instant. The resultant amplitude is?

Question

Accepted Answer

14.1 units. The two waves have the same amplitude, 10, and a phase difference of $\pi/2$. For equal amplitudes $A$ with phase difference $\phi$, the resultant amplitude is $2A\cos(\phi/2)$. Substituting gives $2\cdot10\cdot\cos(\pi/4)=20\cdot\frac{\sqrt2}{2}=14.1$.

Two waves represented by \( y_{1}= \) \( 10 \sin (2000 \pi t) \) and \( y_{2}= \) \( 10 \sin (2000 \pi t+\pi / 2) \) are superimposed at any point at a particular instant. The resultant amplitude is?

Solution

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