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Show eqn E = 100 Sin(2(pi)x/3) Cos 5(pi)t is a mixture of 2

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This question is from the text book 'OPTICS' fourth edition by Eugene Hecht.

Thank you so much for your help.

p.s I hope ,if possible, you could let me have answers as in pdf file or scaned paper(unless I could read or understand the letters that you wrote.. Cause, sometimes it's really hard to read the spelling in the sentence in the answers from the OTA.)

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1. Your first question (7.14) is
to show that the equn E = 100 Sin(2(pi)x/3) Cos 5(pi)t is a mixture of two progressive waves.

Ans : Actually Any prograssive wave can be given with the waveform given by the eqution
E1 = 100 sin (wt-kx)
where w(omega which is also given by 2*(pi)*Frequency) is the angular velocity of the wave
in your equation w is 5(pi)
and K( phase constant which is also given by 2(pi)x/lambda)
in your eqaution k is 2(pi)/3.
Here this equation represents a wave which moves in a medium along positive x axis. If it rebounds at a rigid boundary, the wave form returns in the opposite direction ( i.e. +ve x-axis direction) and also gets a phase inversion ( i.e gets a phase difference of (pi) radians). Hence forth gives another wave
...

Solution Summary

Progressive wave can be given with the waveform given by the equation
E1 = 100 sin (wt-kx)
where w(omega which is also given by 2*(pi)*Frequency) is the angular velocity of the wave
in your equation w is 5(pi)

$2.19