The displacement of two sinusoidal waves is given by the equation $\begin{aligned} & y_1=8 \sin (20 x-30 t)…

The displacement of two sinusoidal waves is given by the equation $\begin{aligned} & y_1=8 \sin (20 x-30 t) \\ & y_2=8 \sin (25 x-40 t) \end{aligned}$ then the phase difference between the waves after time $\mathrm{t}=2 \mathrm{~s}$ and distance $\mathrm{x}=5 \mathrm{~cm}$ will be
  1. 2 radian
  2. 3 radian
  3. 4 radian
  4. 5 radian

Solution

$y_1=8 \sin (20 x-3 t)$ Substituting $x=5 \mathrm{~cm}$ and $t=2 \mathrm{~s}$, $y_1=8 \sin (40)$ Similarly, $y_2=8 \sin (45)$ $\therefore \quad$ phase difference $=45-40=5$ radian *

Asked in: MHT CET 2023 (12 May Shift 1)

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