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Model Paper 5 — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsModel Paper 51 Mark
MCQ
Two waves each of amplitude a and have a phase difference $\frac{\pi}{2}$. The amplitude and frequency of a resultant wave due to their superposition will be
  • A
    2a, $\frac{f}{2}$
  • B
    $\sqrt{2} a , f$
  • C
    $\frac{a}{\sqrt{2}}, \frac{f}{2}$
  • D
    $\frac{a}{\sqrt{2}}, f$
✓

Answer

(b) $\sqrt{2} a , f$
$
\begin{aligned}
& \text { Explanation: } y_1=a \sin 2 \pi f t \\
& y_2=a \sin \left(2 \pi f t+\frac{\pi}{2}\right) \\
& \therefore y=y_1+y_2=2 a \sin \left(2 \pi f t+\frac{\pi}{4}\right) \cos \frac{\pi}{4} \\
& =\frac{2 a}{\sqrt{2}} \sin \left(2 \pi f t+\frac{\pi}{4}\right) \\
& =\sqrt{2} a \sin \left(2 \pi f t+\frac{\pi}{4}\right)
\end{aligned}
$
Hence the resultant wave has amplitude $\sqrt{2} a$ and frequency f.

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