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  • The equation of a simple harmonic progressive wave is given by, <img alt="y=A \sin (100 \pi t-3 x)" src="https://entrancecorner.oncodecogs.com/gif.latex?y%3DA%20%5Csin%20%28100%20%5Cpi%20t-3%2

The equation of a simple harmonic progressive wave is given by, y=A \sin (100 \pi t-3 x)  Find the distance between 2 particles having a phase difference of \frac{\pi}{3}.

Option: 1

\frac{\pi}{9} \, m


Option: 2

\frac{\pi}{18} \, m


Option: 3

\frac{\pi}{6} \, m


Option: 4

\frac{\pi}{3} \, m


Answers (1)

best_answer

Given, y=A \sin (100 \pi t-3 x)\\\\ \text {The general equation-}\\\\ \begin{aligned} & y=A \sin (\omega t-k x) \: and\: k=3 \end{aligned}\\\ \begin{aligned} k= \frac {2 \pi}{\lambda} \\\\ & \lambda= \frac{2 \pi}{k}=\frac{2 \pi}{3} \end{aligned}\\\\ \text { phase difference, } \begin{aligned} \phi & =\pi / 3 \Rightarrow \frac{2 \pi}{3} \cdot x=\frac{\pi}{3} \\ x & =\frac{\pi}{3} \times \frac{\pi}{2 \pi} \\ x & =\frac{\pi}{3} \times \frac{2 \pi}{3 \times 2 \pi} \\ x & =\pi / 9 \mathrm{~m} \end{aligned}

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Kuldeep Maurya

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