Given wave equation

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

Compare this with the standard harmonic wave form:

$y=A\sin(\omega t \pm kx)$

So, $\omega=6\ \text{rad s}^{-1}, \qquad k=0.003\ \text{cm}^{-1}$

Use wave speed relation

The speed of a harmonic wave is

$v=\frac{\omega}{k}$

Therefore,

$v=\frac{6}{0.003}=2000\ \text{cm s}^{-1}$

Convert to SI units

Since $100\ \text{cm}=1\ \text{m}$

$2000\ \text{cm s}^{-1}=\frac{2000}{100}=20\ \text{m s}^{-1}$

Direction note

Because the phase is $(6t+0.003x)$, the wave travels in the negative $x$-direction, but the speed is just the magnitude:

$20\ \text{m s}^{-1}$

Final integer answer

$\boxed{20}$

Comparison with stored answer

Stored correct answer = $20$

Our derived answer also = $20$

Hence, the answer agrees.