# The displacemwent y of a wave travelling in the x - direction is given by where x is expressed in metre and t in second. The speed of the wave­-motion, in ms-1 is  Option 1) Option 2) Option 3) Option 4)

As we learnt in

Wave Speed -

It is distance travelled by the wave in unit time.

- wherein

It is denoted by V

Given wave equation

$y= 10^{-4}\sin \left ( 600t-2x+\frac{\pi }{3} \right )meter$

$Standard\: wave\: equation\: y=a\sin \left ( \omega t-kx+\phi \right )$

Compare them

Angular speed $= \omega = 600\: sec^{-1}$

Propagation constan $= k= 2\: m^{-1}$

$\frac{\omega }{k}= \frac{2\pi \upsilon }{2\pi/\lambda }= \upsilon \lambda = velocity$

$\therefore\: \: velocity\: = \frac{\omega }{k}= \frac{600}{2}= 300\: m/sec$

Correct option is 1.

Option 1)

This is the correct option.

Option 2)

This is an incorrect option.

Option 3)

This is an incorrect option.

Option 4)

This is an incorrect option.

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