A wave is represented by the equation `y=(0.001mm)sin[(50s^-1t+(2.0m^-1)x]`

Options

A. The wave velocity `=100 ms^-1`
B. The wavelength =2.0m
C. the frequencey `=25/piHz`
D. The amplitude =0.001mm

Answer

To solve the problem step by step, we will analyze the given wave equation and extract the necessary parameters to find the wave velocity, frequency, wavelength, and amplitude.

### Step 1: Identify the parameters from the wave equation
The given wave equation is:
\[ y = (0.001 \, \text{mm}) \sin(50 \, \text{s}^{-1} t + (2.0 \, \text{m}^{-1}) x) \]

From this equation, we can identify:
- Amplitude \( A = 0.001 \, \text{mm} \)
- Angular frequency \( \omega = 50 \, \text{s}^{-1} \)
- Wave number \( k = 2.0 \, \text{m}^{-1} \)

### Step 2: Calculate the wave velocity
The wave velocity \( V \) can be calculated using the formula:
\[ V = \frac{\omega}{k} \]

Substituting the values:
\[ V = \frac{50 \, \text{s}^{-1}}{2.0 \, \text{m}^{-1}} = 25 \, \text{m/s} \]

### Step 3: Calculate the frequency
The frequency \( f \) can be calculated from the angular frequency using the formula:
\[ f = \frac{\omega}{2\pi} \]

Substituting the value of \( \omega \):
\[ f = \frac{50 \, \text{s}^{-1}}{2\pi} = \frac{25}{\pi} \, \text{Hz} \]

### Step 4: Calculate the wavelength
The wavelength \( \lambda \) can be calculated using the relationship between wave velocity and frequency:
\[ \lambda = \frac{V}{f} \]

Substituting the values we have:
\[ \lambda = \frac{25 \, \text{m/s}}{\frac{25}{\pi} \, \text{Hz}} = \pi \, \text{m} \approx 3.14 \, \text{m} \]

### Step 5: State the amplitude
The amplitude \( A \) has already been identified from the wave equation:
\[ A = 0.001 \, \text{mm} \]

### Summary of Results
- Wave velocity \( V = 25 \, \text{m/s} \)
- Frequency \( f = \frac{25}{\pi} \, \text{Hz} \)
- Wavelength \( \lambda \approx 3.14 \, \text{m} \)
- Amplitude \( A = 0.001 \, \text{mm} \)