Which of the following equations represents as wave travelling along Y-axis?

Options

A. `x=Asin(ky-omegat)`
B. `y=Asin(kx-omegat)`
C. `y=Asinkycosomegat`
D. `y=Acoskysinomegat`.

Answer

To determine which equation represents a wave traveling along the Y-axis, we need to analyze the standard form of a wave equation.

### Step-by-Step Solution:

1. **Understand the Standard Wave Equation**:
The standard equation for a wave traveling in the Y-direction is given by:
\[ x = A \sin(ky - \omega t) \]
Here, \( A \) is the amplitude, \( k \) is the wave number, \( \omega \) is the angular frequency, \( y \) is the spatial variable along the direction of wave propagation, and \( t \) is time.

2. **Identify the Variables**:
- \( A \): Amplitude of the wave.
- \( k \): Wave number, which is related to the wavelength (\( \lambda \)) by \( k = \frac{2\pi}{\lambda} \).
- \( y \): The variable representing the position along the Y-axis.
- \( t \): Time variable.

3. **Check the Direction of Wave Propagation**:
In the equation \( x = A \sin(ky - \omega t) \), the wave is traveling in the Y-direction because the argument of the sine function includes \( y \) and not \( x \). This indicates that the displacement of the wave is a function of \( y \) and time \( t \).

4. **Evaluate the Options**:
We need to compare the provided options with the standard equation. The correct equation for a wave traveling along the Y-axis should have \( y \) in the sine function and not \( x \).

5. **Select the Correct Option**:
Based on the analysis, the correct equation that represents a wave traveling along the Y-axis is:
\[ x = A \sin(ky - \omega t) \]
This corresponds to option number one.

### Final Answer:
The equation that represents a wave traveling along the Y-axis is:
\[ x = A \sin(ky - \omega t) \]

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