Question

In a stationary wave that from as a result of reflection of waves from an obstacle, the ratio of the amplitude at an antinode to the amplitude at node is 6. What percentage of energy is transmitted?

Solution

Let the incident amplitude be $$a$$ and reflected be $$b$$. Hence, as per the question, $$\dfrac { a+b }{ a-b } =6$$. Hence, $$\dfrac { a }{ b } =\dfrac { 7 }{ 5 }$$.Since energy is proportional to square of amplitude, ratio of reflected energy will be $$\dfrac { { 7 }^{ 2 }-{ 5 }^{ 2 } }{ { 7 }^{ 2 } } 100=\dfrac { 2400 }{ 49 } \approx 49$$.Physics

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