The equation of a wave is
`y=(x,t)=0.05 sin [(pi)/(2)(10x-40t)-(pi)/(4)]m`
find: (a) the wavelength, the frequency and the wave velocity
(b) the participle velocity and acceleration at `x=0.5m`and `t = 0.05s`.

Explanation

To solve the given problem, we will break it down into two parts: (a) finding the wavelength, frequency, and wave velocity; and (b) finding the particle velocity and acceleration at specific values of \(x\) and \(t\).

### Part (a): Finding Wavelength, Frequency, and Wave Velocity

1. **Identify the Wave Equation**:
The given wave equation is:
\[
y(x, t) = 0.05 \sin\left(\frac{\pi}{2}(10x - 40t) - \frac{\pi}{4}\right) \text{ m}
...