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  • Two waves are passing through a region in the same direction at the same time. If the equation  <img alt="y_1=a \sin \frac{2 \pi}{\lambda}(v t-x) \text { and } y_2=b \sin \frac{

Two waves are passing through a region in the same direction at the same time. If the equation 

y_1=a \sin \frac{2 \pi}{\lambda}(v t-x) \text { and } y_2=b \sin \frac{2 \pi}{\lambda}\left[(v t-x)+x_0\right] then the amplitude of the resulting wave for x_0=(\lambda / 2) is

Option: 1

|a-b|


Option: 2

a+b


Option: 3

\sqrt{a^2+b^2}


Option: 4

\sqrt{a^2+b^2+2 a b \cos x}


Answers (1)

best_answer

Let \phi_1 and \phi_2 represent phase angles.

\phi_1=\frac{2 \pi}{\lambda}(v t-x) \quad ; \quad \phi_2=\frac{2 \pi}{\lambda}\left[(v t-x)+x_0\right]

\phi_2-\phi_1=\frac{2 \pi}{\lambda} x_0

\text { But } x_0=\frac{\lambda}{2} \quad \therefore \phi_2-\phi_1=\pi

Hence, phase difference, \phi=\pi so, amplitude of resultant wave 

R=\sqrt{a^2+b^2+2 a b \cos \phi}

=\sqrt{a^2+b^2+2 a b \cos \pi}     [\phi=\pi]

=\sqrt{(a-b)^2}

= a-b

Posted by

Deependra Verma

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