Waves and its Characteristics: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Waves and its Characteristics. Understanding the underlying formula is key to arriving at the correct answer below:

Comparing with $y = A\sin(\omega t - kx)$, we get $A = 3$, $\omega = 25\pi$, and $k = \pi/2$. Maximum particle velocity $v_{p} = A\omega$. Wave velocity $v_{w} = \omega/k$. The ratio is $v_{p}/v_{w} = (A\omega) / (\omega/k) = Ak = 3 \times (\pi/2) = 3\pi/2$.