Which of the following equations represent a transverse wave travelling along- y axis ?

Options

A. `x=A sin( omegat-ky)`
B. `x=A sin ( omegat+ky)`
C. `y_0=A sin (omegat-kx)`
D. `y_0=A sin( omegat+kx)`

Answer

To determine which equation represents a transverse wave traveling along the negative y-axis, we can analyze the standard form of the wave equations.

### Step-by-Step Solution:

1. **Understand the Standard Form of a Transverse Wave:**
The standard equation for a transverse wave traveling along the positive y-axis is given by:
\[ y = A \sin(\omega t - kx) \]
Here, \( A \) is the amplitude, \( \omega \) is the angular frequency, \( k \) is the wave number, \( t \) is time, and \( x \) is the position along the x-axis.

2. **Identify the Direction of Propagation:**
- For a wave traveling in the positive y-direction, the equation is \( y = A \sin(\omega t - kx) \).
- For a wave traveling in the negative y-direction, the equation changes to:
\[ y = A \sin(\omega t + kx) \]

3. **Analyze the Given Options:**
We need to determine which of the provided equations represents a transverse wave traveling along the negative y-axis. The equation should have the form:
\[ y = A \sin(\omega t + ky) \]
This indicates that the wave is moving in the negative y-direction.

4. **Select the Correct Equation:**
From the analysis, if one of the options is:
\[ y = A \sin(\omega t + ky) \]
This equation represents a transverse wave traveling along the negative y-axis.

### Conclusion:
The correct equation representing a transverse wave traveling along the negative y-axis is:
\[ y = A \sin(\omega t + ky) \]