A wave travels on a light string- The equation of the wave is y-A sin kx - wt - 30-180- it is reflected from a heavy string tied to an end of the light string at x- 0- If 64

Energy reflected = 64 Hence, amplitude of reflected wave = √(64/100)A = 0.8A As wave is reflected from a denser medium, phase change of 180^∘ will take place. M ...

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Standard XIII

Physics

Reflection from a Fixed End

A wave travel...

Question

A wave travels on a light string. The equation of the wave is $y = A s i n (k x + w t + 30^{\circ} + 180^{\circ})$ , it is reflected from a heavy string tied to an end of the light string at x= 0. If 64% of the incident energy is reflected then what is the equation of the reflected wave?

y = A s i n (k x - w t + 30^{\circ})

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y = A s i n (k x + w t + 30^{\circ})

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y = 0.8 A s i n (k x - w t + 30^{\circ})

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y = 0.8 A s i n (k x + w t + 30^{\circ})

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Solution

The correct option is C $y = 0.8 A s i n (k x - w t + 30^{\circ})$
Energy reflected = 64% of incident energy
Hence, amplitude of reflected wave $= \sqrt{\frac{64}{100}} A = 0.8 A$
As wave is reflected from a denser medium, phase change of $180^{\circ}$ will take place. Moreover, it will travel along negative x-axis.
Hence, equation of reflected wave is $y = 0.8 A s i n (k x - w t + 30^{\circ})$

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