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QJEEM23Phd818: JEE Main 2023 Physics - Class 11 JEEM23Phd818 Solution: Two simple harmonic waves having equal amplitudes of 8 cm and…

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.

Step-by-Step Verified Solution

AR=A12+A22+2A1A2cos⁡ϕA_{R}=\sqrt{A_{1}^{2}+A_{2}^{2}+2 A_{1} A_{2} \cos \phi}

amp;8=82+82+2×8×8cos⁡ϕamp;⇒cos⁡ϕ=−12amp;⇒ϕ=120∘\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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