JEE MAIN - Physics (2023 - 29th January Morning Shift - No. 18)
Two simple harmonic waves having equal amplitudes of 8 cm and equal frequency of 10 Hz are moving along the same direction. The resultant amplitude is also 8 cm. The phase difference between the individual waves is _________ degree.
Answer
120
Explanation
$A_{R}=\sqrt{A_{1}^{2}+A_{2}^{2}+2 A_{1} A_{2} \cos \phi}$
$$ \begin{aligned} & 8=\sqrt{8^{2}+8^{2}+2 \times 8 \times 8 \cos \phi} \\\\ & \Rightarrow \cos \phi=-\frac{1}{2} \\\\ & \Rightarrow \phi=120^{\circ} \end{aligned} $$
$$ \begin{aligned} & 8=\sqrt{8^{2}+8^{2}+2 \times 8 \times 8 \cos \phi} \\\\ & \Rightarrow \cos \phi=-\frac{1}{2} \\\\ & \Rightarrow \phi=120^{\circ} \end{aligned} $$
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