Choose the correct statements from the following :

Options

A. Any function of the form `y( x, t) = f( vt + x)` represents a travelling wave.
B. The velocity , wavelength and frequency of a wave do not undergo any change when it is reflected from the surface .
C. When an ultrasonic wave travels from air into water , it bends towards the normal to air - water interface.
D. The velocity of sound is generally greater in solids than in gases at `NTP`.

Explanation

To solve the question, we need to analyze each statement provided and determine whether it is correct or incorrect based on the principles of wave mechanics.

### Step-by-Step Solution:

1. **Statement A**: "Any function of the form \( y(x, t) = f(vt + x) \) represents a traveling wave."
- **Analysis**: This statement is correct. The general form of a traveling wave can be expressed as \( y(x, t) = f(vt + x) \), where \( v \) is the wave velocity. This form indicates that the wave travels in the positive x-direction.

2. **Statement B**: "The velocity, wavelength, and frequency of the wave do not undergo any change when it is reflected from the surface."
- **Analysis**: This statement is also correct. When a wave reflects off a boundary in the same medium, its speed, wavelength, and frequency remain unchanged. The reflection does not alter these properties.

3. **Statement C**: "When an ultrasonic wave travels from air into water, it bends toward the normal at the air-water interface."
- **Analysis**: This statement is incorrect. When a wave travels from a medium with a lower speed (air) to a medium with a higher speed (water), it bends away from the normal. Thus, this statement is false.

4. **Statement D**: "The velocity of sound is generally greater in solids than in gases."
- **Analysis**: This statement is correct. The velocity of sound is indeed greater in solids than in gases due to the higher modulus of elasticity in solids, which allows sound waves to propagate faster.

### Conclusion:
- **Correct Statements**: A, B, and D.
- **Incorrect Statement**: C.

### Final Answer:
- **Correct Statements**: A, B, D
- **Incorrect Statement**: C

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