Three transverse waves are represented by
`y_1=A cos (kx-omega t)`
`y_2=A cos (kx+omega t)`
`y_3=A cos (ky-omega t)`
The combination of waves which can produce stationary waves is

Options

A. `y_1 and y_2`
B. `y_2 and y_3`
C. `y_1 and y_3`
D. `y_1,y_2 and y_3`

Explanation

To determine which combination of the given waves can produce stationary waves, we need to analyze the equations of the waves provided in the question:

1. **Identify the given waves:**
- \( y_1 = A \cos(kx - \omega t) \)
- \( y_2 = A \cos(kx + \omega t) \)
- \( y_3 = A \cos(ky - \omega t) \)

2. **Understand the conditions for stationary waves:**
- Stationary waves are formed when two waves of the same frequency and amplitude travel in opposite directions. This means we need one wave moving in the positive x-direction and another wave moving in the negative x-direction.

3. **Analyze the direction of each wave:**
- For \( y_1 = A \cos(kx - \omega t) \):
- This wave travels in the positive x-direction.
- For \( y_2 = A \cos(kx + \omega t) \):
- This wave travels in the negative x-direction.
- For \( y_3 = A \cos(ky - \omega t) \):
- This wave is not in the x-direction; it travels in the y-direction.

4. **Determine which waves can combine to form stationary waves:**
- The combination of \( y_1 \) and \( y_2 \) can produce stationary waves since they are traveling in opposite directions (one in positive x and the other in negative x).
- The wave \( y_3 \) does not contribute to stationary waves in the x-direction, as it is not propagating along the x-axis.

5. **Conclusion:**
- The combination of waves that can produce stationary waves is \( y_1 \) and \( y_2 \).

### Final Answer:
The combination of waves which can produce stationary waves is \( y_1 \) and \( y_2 \).

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