Equation of a progressive wave is given by $y = 0.2\cos\pi\left( 0.04t + .02x - \frac{\pi}{6} \right)$ The distance is expressed in $cm$ and time in second. What will be the minimum distance between two particles having the phase difference of $\pi/2$

Question

Dr. Abubacker · Accepted Answer

(c) Comparing with $y = a\cos{(\omega t + kx - \phi)},$
We get $k = \frac{2\pi}{\lambda} = 0.02\pi \Rightarrow \lambda = 100\ cm$
Also, it is given that phase difference between particles $\Delta\phi = \frac{\pi}{2}.$ Hence path difference between them
$\Delta = \frac{\lambda}{2\pi} 	imes \mathrm{\Delta}\phi = \frac{\lambda}{2\pi} 	imes \frac{\pi}{2} = \frac{\lambda}{4} = \frac{100}{4} = 25\ cm$

Q. Equation of a progressive wave is given by $y = 0.2\cos\pi\left( 0.04t + .02x - \frac{\pi}{6} \right)$ The distance is expressed in $cm$ and time in second. What will be the minimum distance between two particles having the phase difference of $\pi/2$

Explanation

Reviewed by Dr. Abubacker

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