The particles displacement in a wave is given by
`y = 0.2 xx 10^(-5) cos (500 t - 0.025 x)`
where the distances are measured in meters and time in seconds. Now

Options

A. wave velocity is `2 xx 10^(4)ms^(-1)`
B. particles velocity is `2 xx 10^(4)ms^(-1)`
C. initial phase difference is `(pi)/(2)`
D. wavelength of the wave is `(80pi)m`

Explanation

To solve the problem, we need to analyze the wave equation given:

\[ y = 0.2 \times 10^{-5} \cos(500t - 0.025x) \]

### Step 1: Identify the amplitude
The amplitude \( A \) of the wave can be directly read from the equation.

\[ A = 0.2 \times 10^{-5} \, \text{meters} \]

### Step 2: Identify the angular frequency \( \omega \)
The angular frequency \( \omega \) is the coefficient of \( t \) in the cosine function.

\[ \omega = 500 \, \text{rad/s} \]

### Step 3: Identify the wave number \( k \)
The wave number \( k \) is the coefficient of \( x \) in the cosine function.

\[ k = 0.025 \, \text{rad/m} \]

### Step 4: Calculate the wave velocity \( v \)
The wave velocity \( v \) can be calculated using the formula:

\[ v = \frac{\omega}{k} \]

Substituting the values we found:

\[ v = \frac{500}{0.025} = 20000 \, \text{m/s} \]

### Step 5: Calculate the wavelength \( \lambda \)
The wavelength \( \lambda \) can be calculated using the formula:

\[ \lambda = \frac{2\pi}{k} \]

Substituting the value of \( k \):

\[ \lambda = \frac{2\pi}{0.025} = 80\pi \, \text{meters} \]

### Summary of Results
- Amplitude \( A = 0.2 \times 10^{-5} \, \text{m} \)
- Wave velocity \( v = 20000 \, \text{m/s} \)
- Wavelength \( \lambda = 80\pi \, \text{m} \)

### Final Answers
- The wave velocity is \( 2 \times 10^4 \, \text{m/s} \).
- The wavelength is \( 80\pi \, \text{m} \).