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Mechanical Properties Of Fluids

Question
CBSEENPH11020560
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The equation of a simple harmonic wave is given by
straight y equals 3 space sin straight pi over 2 space left parenthesis 50 straight t minus straight x right parenthesis
where x nd y are in metres and t is in seconds. The ratio of maximum particle celocity of the wave velocity is

  • 2π

  • 3π/2

  • 3π

  • 2π/3

Solution

B.

3π/2

We know that
straight v subscript max space equals aω and space straight v equals nλ therefore comma space straight v subscript max over straight v space equals space aω over nλ equals fraction numerator straight a left parenthesis 2 πn right parenthesis over denominator nπ end fraction space equals space fraction numerator 2 πa over denominator straight lambda end fraction equals fraction numerator 2 πa over denominator 2 straight pi divided by straight a end fraction space equals ka space equals space straight pi over 2 space straight x space 3 space equals space fraction numerator 3 straight pi over denominator 2 end fraction

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