The equation of a transverse wave travelling along a string is $$y(x,t)=4.0\sin[20\times 10^{-3}x+600t]mm$$ where x is in mm and t is in second. The velocity of the wave is :

Wave equation: $$y = 4.0\sin[20 \times 10^{-3}x + 600t]$$ mm, where x in mm, t in s.

$$k = 20 \times 10^{-3}$$ mm$$^{-1}$$ = 20 m$$^{-1}$$ (converting: 0.02 per mm = 20 per m).

$$\omega = 600$$ rad/s.

Velocity $$v = -\frac{\omega}{k} = -\frac{600}{20} = -30$$ m/s.

The negative sign indicates the wave travels in the negative x-direction (since the equation has $$+kx$$).

The correct answer is Option 2: -30 m/s.