Final answer:
The ratio of maximum particle velocity to wave velocity in the given equation is 50. Therefore, the correct option is A.
Step-by-step explanation:
The equation represents a wave with a sinusoidal shape, where y is the displacement of the wave at a given point in space and time. The given equation, y = 10 sin(50t + 5x), is written in terms of time (t) and position (x).
The ratio of the maximum particle velocity to wave velocity can be found by taking the derivative of the displacement equation with respect to time, which gives the velocity equation. In this case, the velocity equation is v = 10(50) cos(50t + 5x). The maximum velocity occurs when cos(50t + 5x) = 1, so the maximum velocity is 10(50) = 500 m/s.
Since wave velocity is given by the equation v = ω/k, where ω is the angular frequency and k is the wave number, the ratio of maximum particle velocity to wave velocity is 500/10 = 50 (Option A).