Two simple harmonic waves having equal amplit | vedclass

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(A) The resultant amplitude $R$ of two waves with equal amplitude $A$ and phase difference $\Delta \phi$ is given by the formula: $R = 2A \cos \left(\

Vedclass · Accepted Answer

$120$

Vedclass · Answer

(A) The resultant amplitude $R$ of two waves with equal amplitude $A$ and phase difference $\Delta \phi$ is given by the formula: $R = 2A \cos \left(\frac{\Delta \phi}{2}\right)$.Given $A = 8\,cm$ and $R = 8\,cm$.Substituting the values: $8 = 2(8) \cos \left(\frac{\Delta \phi}{2}\right)$.This simplifies to: $1 = 2 \cos \left(\frac{\Delta \phi}{2}\right)$,which means $\cos \left(\frac{\Delta \phi}{2}\right) = \frac{1}{2}$.Since $\cos(60^{\circ}) = \frac{1}{2}$,we have $\frac{\Delta \phi}{2} = 60^{\circ}$.Therefore,the phase difference $\Delta \phi = 120^{\circ}$.

Two simple harmonic waves having equal amplitudes of $8\,cm$ and equal frequency of $10\,Hz$ are moving along the same direction. The resultant amplitude is also $8\,cm$. The phase difference between the individual waves is $..................$ degree.

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