A transverse harmonic wave on a string is given by

$y(x,t) = 5\sin (6t + 0.003x)$

where x and y are in cm and t in sec. The wave velocity is _______________ ms$^{-1}$.

<p>The general equation for a transverse harmonic wave on a string is given by:</p> <p>$y(x,t) = A \sin(kx - \omega t + \phi)$</p> <p>where $A$ is the amplitude of the wave, $k$ is the wave number, $\omega$ is the angular frequency, and $\phi$ is the phase constant. The wave velocity $v$ is related to the wave number and angular frequency by the formula:</p> <p>$v = \frac{\omega}{k}$</p> <p>Comparing the given equation with the general equation, we can see that:</p> <p>$A = 5 \, \text{cm}$</p> <p>$k = 0.003 \, \text{cm}^{-1}$</p> <p>$\omega = 6 \, \text{rad/s}$</p> <p>Therefore, the wave velocity is:</p> <p>$$ v = \frac{\omega}{k} = \frac{6}{0.003} = 2000 \, \text{cm/s} = \boxed{20 \, \text{m/s}} $$</p>