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Question

The equation of a plane progressive wave is y=0.09sin 8π(tx20). When it is reflected at rigid support, its amplitude become 23rd of its previous value. Then the equation of the reflected wave is 
  1. y=0.09sin8π(tx20)
  2. y=0.09sin8π(t+x20)
  3. y=0.06sin8π(t+x20)
  4. y=0.06sin8π(t+x20)


Solution

The correct option is D y=0.06sin8π(t+x20)
When wave gets reflected at rigid support, it undergoes a phase change of π and travels in opposite direction but its wavenumber and angular frequency remain same.
It is given, amplitude of reflected wave become 23rd of its previous value.
So, amplitude of reflected wave, Ar=23×0.09=0.06 cm 
Hence, 
Reflected wave equation is
y=0.06sin8π(t+x20+π)
y=0.06sin8π(t+x20)

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