A wave is represented by the equation
`y=0.1 sin (100pit-kx)`
If wave velocity is `100 m s^(-1)`, its wave number is equal to

Options

A. `1 m^(-1)`
B. `2 m^(-1)`
C. `pi m^(-1)`
D. `2pi m^(-1)`

Answer

To find the wave number \( k \) from the given wave equation \( y = 0.1 \sin(100\pi t - kx) \) and the wave velocity \( v = 100 \, \text{m/s} \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Angular Frequency (\( \omega \))**:
The wave equation is in the form \( y = A \sin(\omega t - kx) \). From the equation, we can see that:
\[ \omega = 100\pi \]

2. **Use the Wave Velocity Formula**:
The relationship between wave velocity \( v \), angular frequency \( \omega \), and wave number \( k \) is given by:
\[ v = \frac{\omega}{k} \]
Rearranging this formula to solve for \( k \) gives:
\[ k = \frac{\omega}{v} \]

3. **Substitute the Values**:
Now, substitute the values of \( \omega \) and \( v \) into the equation:
\[ k = \frac{100\pi}{100} \]

4. **Simplify the Expression**:
Simplifying the expression gives:
\[ k = \pi \, \text{m}^{-1} \]

5. **Conclusion**:
Therefore, the wave number \( k \) is:
\[ k = \pi \, \text{m}^{-1} \]

### Final Answer:
The wave number \( k \) is \( \pi \, \text{m}^{-1} \).

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