Equation of a plane progressive wave is given by y=0.6 2 (t- x 2 … - Vidyadip

MCQ

Equation of a plane progressive wave is given by $\text{y}=0.6\sin2\pi\Big(\text{t}-\frac{\text{x}}{2}\Big).$ On reflection from a denser medium its amplitude becomes 2/3 of the amplitude of the incident wave. The equation of the reflected wave is:

A
$\text{y}=0.6\sin2\pi\Big(\text{t}+\frac{\text{x}}{2}\Big)$
✓
$\text{y}=-0.4\sin2\pi\Big(\text{t}+\frac{\text{x}}{2}\Big)$
C
$\text{y}=0.4\sin2\pi\Big(\text{t}+\frac{\text{x}}{2}\Big)$
D
$\text{y}=-0.4\sin2\pi\Big(\text{t}-\frac{\text{x}}{2}\Big)$

✓

Answer

Correct option: B.

$\text{y}=-0.4\sin2\pi\Big(\text{t}+\frac{\text{x}}{2}\Big)$

After reflection of wave changes by phase 180°
$\text{y}_\text{i}=0.6\sin2\pi\Big[\text{t}+\frac{\text{x}}{2}\Big]$
$\text{y}_\text{r}\Big(\frac{2}{3}\times0.6\Big)\sin2\pi\Big[\pi+\text{t}+\frac{\text{x}}{2}\Big]$
$\text{y}_\text{r}=-0.4\sin2\pi\Big(\text{t}+\frac{\text{x}}{2}\Big).$ Hence verifies the option (b).

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