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Mechanical Properties Of Fluids

Question
CBSEENPH11020309
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The transverse displacement y(x,t) of a wave on a string is given by
straight y left parenthesis straight x comma straight t right parenthesis space equals space straight e to the power of negative left parenthesis ax squared plus bt squared space plus space 2 square root of ab space xt right parenthesis end exponent
This represents a

  • wave moving in +x direction with speed square root of straight a over straight b end root

  • wave moving in -x direction with speed square root of b over a end root

  • standing wave frequency square root of straight a

  • Standing wave of frequency square root of 1 over straight b end root

Solution

B.

wave moving in -x direction with speed square root of b over a end root

Given wave is,
straight y space left parenthesis straight x comma straight t right parenthesis space equals space straight e to the power of negative left parenthesis ax squared space plus bt squared space plus 2 square root of ab space xt right parenthesis end exponent space equals space straight e to the power of negative left parenthesis square root of ax space plus square root of bt right parenthesis squared end exponent It space is space straight a space function space of space type space straight y space equals space straight f left parenthesis ωt space plus kx right parenthesis space equals space straight f open parentheses straight t minus straight x over straight v close parentheses Where space straight v space is space the space wave space velocity. therefore space straight y space left parenthesis straight x comma straight t right parenthesis space represents space wave space travelling space along space minus straight x space direction Speed space of space wave space space equals space straight omega over straight k space equals space fraction numerator square root of straight b over denominator square root of straight a end fraction space equals space square root of straight b over straight a end root

Some More Questions From Mechanical Properties of Fluids Chapter

Can sound travel in vacuum?

Can two persons hear each other on the moon? Explain.

Can electromagnetic wave propagate in vacuum?

Can we listen in vacuum?

Which of the two moves forward during wave motion - particle or disturbance?

What type of wave is sound wave when it travels in air?

What type of wave is sound wave when it travels in solids?

Which of the two - sound or light is longitudinal in nature?

In what form the sound travels in air?

Define frequency.

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