Equation of a plane progressive wave is given by y=0.6sin2 $\mathit{\pi }\left(\mathit{t}-\frac{\mathit{x}}{2}\right)$ . 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) y=0.6sin2 $\mathit{\pi }\left(\mathit{t}+\frac{\mathit{x}}{2}\right)$

(b) y=-0.4sin2 $\mathit{\pi }\left(\mathit{t}+\frac{\mathit{x}}{2}\right)$

(c) y=0.4sin2 $\mathit{\pi }\left(\mathit{t}+\frac{\mathit{x}}{2}\right)$

(d) 0.4sin2 $\mathit{\pi }\left(\mathit{t}-\frac{\mathit{x}}{2}\right)$

<p><span data-teams="true">This is a multiple choice answer as classified in NCERT Exemplar</span></p><p> (b) Amplitude of reflected wave</p><p>A_f=<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> </mfrac> <mo>×</mo> <msub> <mrow> <mrow> <mi>A</mi> </mrow> </mrow> <mrow> <mrow> <mi>i</mi> </mrow> </mrow> </msub> </math> </span>=2 (0.6)/3=0.4 units</p><p>Equation of incident wave</p><p>Y_i=0.6sin2<span contenteditable="false"> <math> <mi>π</mi> <mfenced separators="|"> <mrow> <mrow> <mi>t</mi> <mo>-</mo> <mfrac> <mrow> <mrow> <mi>x</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> </mrow> </mrow> </mfenced> </math> </span></p><p>For reflected wave&nbsp;</p><p>y_r=A_rsin2<span contenteditable="false"> <math> <mi>π</mi> </math> </span> (t+x/2+<span contenteditable="false"> <math> <mi>π</mi> </math> </span>)</p><p>Y_r=-0.4sin2<span contenteditable="false"> <math> <mi>π</mi> <mfenced separators="|"> <mrow> <mrow> <mi>t</mi> <mo>+</mo> <mfrac> <mrow> <mrow> <mi>x</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> </mrow> </mrow> </mfenced> </math> </span></p>

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