Equation of a progressive wave is given by $y = 0.2\cos \pi \left( {0.04t + 0.02x - \frac{\pi }{6}} \right)$The distance is expressed in $cm$ and time in second. What will be the minimum distance between two particles having the phase difference of $\pi /2$ ...... $cm$
Medium
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(c) Comparing with $y = a\cos (\omega t + kx - \phi )$,
We get $k = \frac{{2\pi }}{\lambda } = 0.02\, \Rightarrow \,\lambda = 100\,cm$
Also, it is given that phase difference between particles $\Delta \phi = \frac{\pi }{2}.$
Hence path difference between them
$\Delta = \frac{\lambda }{{2\pi }} \times \Delta \phi = \frac{\lambda }{{2\pi }} \times \frac{\pi }{2} = \frac{\lambda }{4} = \frac{{100}}{4} = 25\,cm$
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