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 step by step, we will analyze the wave equation and extract the required parameters.

### Given Wave Equation:
\[ y(x, t) = 0.05 \sin\left(\frac{\pi}{2}(10x - 40t) - \frac{\pi}{4}\right) \]

### Step 1: Rewrite the Wave Equation
We can rewrite the wave equation in a more standard form:
\[ y(x, t) = 0.05 \sin\left(5\pi x - 20\pi t - \frac{\pi}{4}\right) \]
...