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At t = 0, a tranverse wave pulse travelling in +ve  x-direction, with speed of 2 m/s by the function y = \frac{6}{x^{2}}, x \neq 0. Transverse velocity of the particle at x = 2 m and t = 2s is 

  • Option 1)

    3 m/s

  • Option 2)

    -3 m/s

  • Option 3)

    8 m/s

  • Option 4)

    -8 m/s

 

Answers (1)

y [ x , t = 0 ] = \frac{6}{x^{2}} ,   y [x,t] = \frac{6}{(x- 2t)^{2}}

\frac{dy}{dt} = \frac{24}{(x- 2t)^{3}} at x = 2 , t = 2

vy = \frac{24}{(-z)^{3}} = -3 m/s

 

Relation between phase velocity and wave speed -

V_{P}= -V\: \frac{dy}{dx}

- wherein

V_{P}= particle velocity

V = wave velocity

\frac{dy}{dx}= slope of curve

 

 

 

 


Option 1)

3 m/s

This is incorrect.

Option 2)

-3 m/s

This is correct.

Option 3)

8 m/s

This is incorrect.

Option 4)

-8 m/s

This is incorrect.

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subam

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