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Two waves having equation x_{1}=4 \sin \left(\omega t-k x+\varphi_{1}\right), \quad x_{2}=4 \sin \left(\omega t-k x+\varphi_{2}\right) If in the resultant ware the frequency and amplitude remain equal to the amplitude of superimposing waves, the Phase difference between them 

Option: 1

\varphi=\frac{2 \pi}{5}


Option: 2

\varphi=\frac{2 \pi}{3}


Option: 3

\varphi=\frac{3 \pi}{2}


Option: 4

None of above


Answers (1)

best_answer

$$ \begin{aligned} & x_{1}=4 \sin \left(\omega t-k x+\varphi_{1}\right) \\ & x_{2}=4 \sin \left(\omega t-k x+\varphi_{2}\right) \\ & A_{1}=A_{2}=A=a \\ & A^{2}=A_{1}^{2}+A_{2}^{2}+2 A_{1} A_{2} \cos \varphi \\ & a^{2}=a^{2}+a^{2}+2 a^{2} \cos \varphi \\ & -a^{2}=2 a^{2} \cot \varphi \\ & \cos \varphi=\frac{-1}{2} \\ & \varphi=120 \\ & \varphi=120 \times \frac{\pi}{180}=\frac{2 \pi}{3} \\ & \varphi=\frac{2 \pi}{3} \end{aligned}

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Sanket Gandhi

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