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13. oscillations — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics13. oscillations1 Mark
MCQ
Two particles P and Q describe S.H.M. of same amplitude $a$, same frequency $f$ along the same straight line. The maximum distance between the two particles is a $\sqrt{2}$.The initial phase difference between the particle is -
  • A
    $0$
  • ✓
    $\pi / 2$
  • C
    $\pi / 6$
  • D
    $\pi / 3$
✓

Answer

Correct option: B.
$\pi / 2$
b
(b)

$x _1= a \sin \left(\omega t +\phi_1\right), x _2= a \sin \left(\omega t +\phi_2\right)$

$\left| x _1- x _2\right|=2 a \sin \left(\omega t +\frac{\phi_1+\phi_2}{2}\right) \cos \left(\frac{\phi_1-\phi_2}{2}\right)$

To maximize $\left|x_1-x_2\right|: \sin \left(\omega t+\frac{\phi_1+\phi_2}{2}\right)=1$

$\Rightarrow a \sqrt{2}=2 a \times 1 \times \cos \left(\frac{\phi_1-\phi_2}{2}\right)$

$\Rightarrow \frac{1}{\sqrt{2}}=\cos \left(\frac{\phi_1-\phi_2}{2}\right) \Rightarrow \frac{\pi}{4}=\frac{\phi_1-\phi_2}{2}$

$\Rightarrow \phi_1-\phi_2=\frac{\pi}{2}$

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