Two sound waves each of wavelength lambda and | vedclass

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(A) The path difference is given as $\Delta x = \lambda/3$.The phase difference $\phi$ is related to path difference by the formula $\phi = \frac{2\pi

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(A) The path difference is given as $\Delta x = \lambda/3$.The phase difference $\phi$ is related to path difference by the formula $\phi = \frac{2\pi}{\lambda} 	imes \Delta x$.Substituting the value,$\phi = \frac{2\pi}{\lambda} 	imes \frac{\lambda}{3} = \frac{2\pi}{3} = 120^{\circ}$.The resultant amplitude $R$ of two waves with equal amplitude $A$ is given by $R = \sqrt{A^2 + A^2 + 2A^2 \cos \phi}$.Substituting $\phi = 120^{\circ}$ and $\cos(120^{\circ}) = -0.5$:$R = \sqrt{A^2 + A^2 + 2A^2(-0.5)}$$R = \sqrt{2A^2 - A^2}$$R = \sqrt{A^2} = A$.

Two sound waves each of wavelength $\lambda$ and having the same amplitude $A$ from two sources $S_1$ and $S_2$ interfere at a point $P$. If the path difference $S_2P - S_1P = \lambda/3$,then the amplitude of the resultant wave at point $P$ will be $[\cos(120^{\circ}) = -0.5]$.

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