Question

Two particles perform linear simple harmonic motion along the same path of length $2A$ and period $T$ as shown in the graph below. The phase difference between them is __________.

• A. Zero rad
• B. $\frac{\pi }{4}$ rad
• C. $\frac{\pi }{2}$ rad
• D. $\frac{3\pi }{4}$ rad

Answer 1

Answer: (B)

$\frac{\pi }{4}$ rad

Let the equation of waves be $Asin(\omega t+\varphi )$.

For wave with peak at $t=0$, the equation becomes,

$y=Asin(\omega t+{90}^{\circ })$

For the wave with displacement $\frac{A}{\sqrt{2}}$ at $t=0$,

$\frac{A}{\sqrt{2}}=Asin\left(\varphi \right)$

$⟹\varphi ={45}^{\circ }=\frac{\pi }{4}$
Hence this is the phase difference between the waves.