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 A travelling harmonic wave is represented by the equation y(x,t) = 10-3 sin (50t + 2x) , where x and y are in meter and t is in seconds. Which of the following is a correct statement about the wave ?

  • Option 1)

    The wave is propagating along the negative x-axis with speed 100 ms-1 .

  • Option 2)

    The wave is propagating along the positive x-axis with speed 25 ms-1 .

  • Option 3)

    The wave is propagating along the positive x-axis with speed 100 ms-1 .

  • Option 4)

     The wave is propagating along the negative x-axis with speed 25 ms-1 .

Answers (1)

best_answer

 

Speed of sinusoidal wave -

Wave Speed

\tfrac{dx}{dt}= V=\frac{\omega }{k}
 

- wherein

\omega = 2\pi \nu

K= \frac{2\pi }{\lambda }

\gamma =10^{3} \, sin\left ( 50t+2x \right )

general ea^{n}

\gamma =a\, sin\left ( wt+kx \right )

wave is moving along

 -ve X-Axis with speed V

&  v=\frac{w}{k}=\frac{50}{2}=25\, m/sec

 


Option 1)

The wave is propagating along the negative x-axis with speed 100 ms-1 .

Option 2)

The wave is propagating along the positive x-axis with speed 25 ms-1 .

Option 3)

The wave is propagating along the positive x-axis with speed 100 ms-1 .

Option 4)

 The wave is propagating along the negative x-axis with speed 25 ms-1 .

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