The equation of a progressive wave is `Y=asin(omegat-kx)`, then the velocity of the wave is

Options

A. `komega`
B. `k//omega`
C. `omega//k`
D. `aomega`

Answer

To find the velocity of the wave given the equation \( Y = a \sin(\omega t - kx) \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Wave Equation**: The given wave equation is \( Y = a \sin(\omega t - kx) \).
- Here, \( a \) is the amplitude, \( \omega \) is the angular frequency, \( t \) is time, \( k \) is the wave number, and \( x \) is the position.

2. **Understand the Terms**: In the wave equation, the term \( \omega t \) represents the time-dependent part, and \( kx \) represents the position-dependent part of the wave.

3. **Use the Velocity Formula**: The velocity \( v \) of a wave can be calculated using the formula:
\[ v = \frac{\text{Coefficient of } t}{\text{Coefficient of } x} \]
In our equation, the coefficient of \( t \) is \( \omega \) and the coefficient of \( x \) is \( k \).

4. **Calculate the Velocity**: Substituting the coefficients into the formula:
\[ v = \frac{\omega}{k} \]
This gives us the velocity of the wave.

5. **Final Result**: Therefore, the velocity of the wave is:
\[ v = \frac{\omega}{k} \]