Question 279: Waves Optics

Question

Two sound waves each of wavelength ' $\lambda$ ' and having the same amplitude ' $A$ ' from two source ' $\mathrm{S}_1$ ' and ' $\mathrm{S}_2$ ' interfere at a point P . If the path difference, $\mathrm{S}_2 \mathrm{P}-\mathrm{S}_1 \mathrm{P}=\lambda / 3$ then the amplitude of resultant wave at point ' P ' will be $\left[\cos \left(120^{\circ}\right)=-0.5\right]$

Accepted Answer

Path difference $=\frac{\lambda}{3}$
$	herefore \quad$ Phase difference $=\frac{2 \pi}{\lambda} 	imes \frac{\lambda}{3}=\frac{2 \pi}{3}=120^{\circ}$
Resultant amplitude
$$R=\sqrt{A_1^2+A_2^2+2 A_1 A_2 \cos 	heta}$$
$$\begin{array}{ll} 
& 	ext { Since, } A_1=A_2 \
	herefore & R=\sqrt{A^2+A^2+2 A^2 \cos 120^{\circ}} \
& R=\sqrt{A^2+A^2+2 A^2 	imes\left(-\frac{1}{2}ight)} \
	herefore & R=A
\end{array}$$

Answer

$\mathrm{A}$

Answer

$\mathrm{2 A}$

Answer

$\frac{\mathrm{A}}{2}$

Answer

$\frac{3 \mathrm{A}}{2}$

Waves Optics

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