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(D) The resultant amplitude $A_R$ of two superimposing waves with amplitudes $a_1$ and $a_2$ and phase difference $\phi$ is given by: $A_R = \sqrt{a_1

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$\sqrt{2} A; \omega$

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(D) The resultant amplitude $A_R$ of two superimposing waves with amplitudes $a_1$ and $a_2$ and phase difference $\phi$ is given by: $A_R = \sqrt{a_1^2 + a_2^2 + 2a_1a_2 \cos \phi}$ Given $a_1 = a_2 = A$ and $\phi = \pi / 2$: $A_R = \sqrt{A^2 + A^2 + 2A^2 \cos(\pi / 2)}$ Since $\cos(\pi / 2) = 0$,we get: $A_R = \sqrt{2A^2} = \sqrt{2} A$ When two waves of the same frequency superimpose,the resultant wave has the same frequency as the individual waves. Therefore,the resultant frequency is $\omega$.

Two waves have the same amplitude $A$ and the same frequency $\omega$. If the phase difference between them is $\pi / 2$,what are the resultant amplitude and the resultant frequency when they superimpose at a point?

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