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  • Two waves are propagating to the point P by two sources A and B of equal frequency . The amplitude of every wave at P is a and the phase of A is ahead by <img alt="\mathrm{\frac{\pi }{3}}" src

Two waves are propagating to the point P by two sources A and B of equal frequency . The amplitude of every wave at P is a and the phase of A is ahead by \mathrm{\frac{\pi }{3}} than that of B and the distance AP is greater than BP by 50 cm.Then the resulting amplitude at the point P will be, if the wavelength is 1 m

Option: 1

2 a


Option: 2

a \sqrt{3}


Option: 3

a \sqrt{2}


Option: 4

a


Answers (1)

best_answer

Path difference, \mathrm{\Delta x=50 \mathrm{~cm}=\frac{1}{2} \mathrm{~m}}

\mathrm{\therefore } Phase difference, \mathrm{\begin{aligned} & \Delta \phi=\frac{2 \pi}{\lambda} \times \Delta x \\ & \Delta \phi=\frac{2 \pi}{1} \times \frac{1}{2}=\pi \end{aligned} }

Total phase difference \mathrm{=\pi-\frac{\pi}{3}=\frac{2 \pi}{3}}

Now, \mathrm{A=\sqrt{a^2+a^2+2 a^2 \cos \left(\frac{2 \pi}{3}\right)}=a}

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