Question

The phase difference between two SHM $y_{1}=10 \,sin$
$\left(10 \pi t+\frac{\pi}{3}\right)$ and $y_{2}=12\, \sin \left(8 \pi t+\frac{\pi}{4}\right)$ at $t=0.5\, s$ is

• A. $\frac{11 \pi}{12}$
• B. $\frac{13 \pi}{12}$
• C. $\pi$
• D. $\frac{17 \pi}{12}$

Answer 1

Answer: (B)

Phase for 1st SHM: $\phi_{1}=10 \pi t+\frac{\pi}{3}$
Phase for 2nd SHM: $\phi_{2}=8 \pi t+\frac{\pi}{4}$
Phase difference: $\Delta \phi=\phi_{1}-\phi_{2}=2 \pi t+\frac{\pi}{12}$
Put $t=0.5 \,s$
$\Delta \phi=2 \pi(0.5)+\frac{\pi}{12}=\frac{13 \pi}{12}$