The equation of simple harmonic wave is given by:

y = 3\sin \frac{\pi } {2}\left( {50\text{t} - x} \right)

where x and y are in metres and t is in seconds. The ratio of maximum particle velocity to the wave velocity is:

  • Option 1)

    \frac{3} {2}\pi

  • Option 2)

    3\pi

  • Option 3)

    \frac{2} {3}\pi

  • Option 4)

    2\pi

 

Answers (1)

As we discussed in

Y\:=\:3Sin\frac{\pi}{2}(50+-x)

Compare with standard wave equation

Y\:=\:aSin(wt-Kx)

Wave velocity = V\:=\:\frac{W}{K}\:=\:\frac{25\pi}{\frac{\pi}{2}}\:=50\:ms^{-1}

The velocity of particle

V_{p}\:=\:\frac{dy}{dt}\:=\:75\pi Cos\:(25\pi t-\frac{\pi}{2}x)

V_{Pmax}\:=\:75\pi

\frac{V_{Pmax}}{V}\:=\:\frac{75\pi}{50}\:=\:\frac{3\pi}{2}


Option 1)

\frac{3} {2}\pi

This option is correct.

Option 2)

3\pi

This option is incorrect.

Option 3)

\frac{2} {3}\pi

This option is incorrect.

Option 4)

2\pi

This option is incorrect.

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