A plane wave `y =a sin (bx + ct)` is incident on a surface. Equation of the reflected wave is `y' = a' sin(ct-bx)`. Which of the following statements is not correct ?

Options

A. The wave is incident on the surface normally
B. Reflecting surface is y-z plane
C. Medium, in which incident wave is travelling is denser than the other medium
D. a' cannot be greater than a

Answer

To solve the problem, we need to analyze the given wave equations and the statements related to them. The incident wave is given by \( y = a \sin(bx + ct) \) and the reflected wave is given by \( y' = a' \sin(ct - bx) \). We need to determine which statement is not correct regarding these waves.

### Step 1: Understand the Direction of Waves
The incident wave \( y = a \sin(bx + ct) \) is traveling in the negative x-direction, as indicated by the \( +ct \) term. The reflected wave \( y' = a' \sin(ct - bx) \) is traveling in the positive x-direction, as indicated by the \( -bx \) term.

**Hint:** Identify the direction of wave propagation from the wave equation.

### Step 2: Analyze the Reflecting Surface
The problem states that the wave is incident normally on a surface. When a wave reflects off a surface normally, it returns along its original path. This means that the angle of incidence is equal to the angle of reflection, which is 0 degrees in this case.

**Hint:** Recall the law of reflection for waves.

### Step 3: Consider the Reflecting Surface Type
The reflecting surface is mentioned to be the yz-plane (where \( x = 0 \)). This is a valid assumption, as the wave reflects back into the medium from which it originated.

**Hint:** Check the geometry of the wave and the surface.

### Step 4: Phase Change upon Reflection
When a wave reflects off a boundary, it may experience a phase change. For a wave reflecting off a fixed boundary, there is typically a phase change of \( \pi \) (or 180 degrees). However, if the reflecting surface is free, there is no phase change. The problem states that if \( \phi = 0 \), then there is no phase change.

**Hint:** Understand the conditions under which phase changes occur upon reflection.

### Step 5: Energy Reflection and Amplitude
If the reflecting surface is perfectly elastic, all the incident energy is reflected back. However, if part of the wave is refracted into another medium, the amplitude of the reflected wave \( a' \) will be less than the amplitude of the incident wave \( a \). Thus, \( a' \) can never be greater than \( a \).

**Hint:** Relate the amplitude of reflected waves to energy conservation principles.

### Conclusion
After analyzing all the statements, we find that:

1. The direction of the incident and reflected waves is correct.
2. The description of the reflecting surface being the yz-plane is correct.
3. The statement about phase change is also correct.
4. The statement regarding the amplitude of the reflected wave being less than or equal to the incident wave is correct.

Since all statements are correct, the question may be misleading or incorrectly framed. However, if we must choose one that is "not correct," it would be the one that implies \( a' \) can never be greater than \( a \) under all circumstances, as this is only true if some energy is refracted.

### Final Answer
All statements are correct, but if forced to choose, the statement about the amplitude could be seen as misleading.