The displacement y (in cm) produced by a simple harmonic wave is given by y= \frac{10}{\pi}\sin(2000 \pi t- \frac{\pi x}{17})the periodic time and maximum velocity of the particles in the medium will respectively be

  • Option 1)

    10^{-3}sec and 330 m/s

  • Option 2)

    10^{-4} sec and 20 m/s

  • Option 3)

    10^{-3} sec and 200 m/s

  • Option 4)

    10^{-2} sec and 2000 cm/s.

 

Answers (1)

As we learnt in 

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

 

 y=\frac{10}{\pi}.sin(2000\pi t-\frac{\pi x}{17})

\omega = 2000 \pi\:\:\:=>T=\frac{2\pi}{\omega}=\frac{1}{1000}=10^{-3}\:sec

& particle velocity V_{p}=\frac{dy}{dt}

V_{p}=\frac{dy}{dt}=\frac{10}{\pi}.(2000 \pi).cos(2000 \pi t-\frac{\pi\:x}{17})

V_{p}^{max}=\frac{10}{\pi}\times 2000 \pi=\:20,000\:cm/s\:=200\:m/sec

 


Option 1)

10^{-3}sec and 330 m/s

This option is incorrect.

Option 2)

10^{-4} sec and 20 m/s

This option is incorrect.

Option 3)

10^{-3} sec and 200 m/s

This option is correct.

Option 4)

10^{-2} sec and 2000 cm/s.

This option is incorrect.

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