A simple harmonic progressive wave is represented by the equation : $y=8\mathrm{sin}2\pi \left(0.1x-2t\right)$ where x and y are in cm and t is in seconds. At any instant the phase difference between two particles separated by 2.0 cm in the x-direction is

(1) 18°

(2) 36°

(3) 54°

(4) 72°

(4) From the given equation $k=0.2\pi$

$\frac{2\pi }{\lambda }=0.2\pi ⇒\lambda =10$ cm

$\Delta \varphi =\frac{2\pi }{\lambda }\text{\hspace{0.17em}}\Delta x=\frac{2\pi }{10}×2=\frac{2\pi }{5}={72}^{o}\text{\hspace{0.17em}}$

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