Physics - Wave on String Question with Solution | TestHub

The standard wave equation is $y(x,t)=A\sin (kx-\omega t)$ or $y(x,t)=A\sin (\omega t-kx)$. Comparing $y(x,t)=0.03\sin (10\pi t-\pi x)$ with $y(x,t)=A\sin (\omega t-kx)$, we get $\omega =10\pi \text{ rad/s}$ and $k=\pi \text{ rad/m}$. The wave speed is $v=\frac{\omega }{k}=\frac{10\pi }{\pi }=10\text{ m/s}$.

Since the coefficients of $t$ and $x$ have opposite signs ($+10\pi t$ and $-\pi x$), the wave propagates in the positive $x$ -direction.