A wave enters to water from air. In air frequency, wavelength, intensity and velocity `n_(1),lambda_(1),I_(1) and v_(1)` respectively.In water the corresponding quantities are `n_(2),lambda_(2),I_(2) and v_(2)` respectively, then

Options

A. `l_(1)=l_(2)`
B. `n_(1)=n_(2)`
C. `v_(1)=v_(2)`
D. `lambda_(1)=lambda_(2)`

Answer

To solve the problem regarding the behavior of a wave as it transitions from air to water, we will analyze the relationships between frequency, wavelength, intensity, and velocity in different media.

### Step-by-Step Solution:

1. **Understanding Wave Properties**:
- When a wave travels from one medium to another, certain properties change while others remain constant. The frequency of the wave is one property that remains unchanged when moving between different media.

**Hint**: Remember that frequency is determined by the source of the wave and does not change when the wave enters a different medium.

2. **Frequency in Air and Water**:
- Let the frequency in air be denoted as \( n_1 \) and in water as \( n_2 \). Since frequency does not change, we have:
\[ n_1 = n_2 \]

**Hint**: Frequency is constant across different media.

3. **Velocity Change**:
- The velocity of the wave changes when it enters a new medium. Let the velocity in air be \( v_1 \) and in water be \( v_2 \). Therefore, we have:
\[ v_1 \neq v_2 \]

**Hint**: The speed of a wave is affected by the medium through which it travels.

4. **Wavelength Change**:
- The relationship between velocity, frequency, and wavelength is given by the equation:
\[ v = n \lambda \]
- In air, this can be expressed as:
\[ v_1 = n_1 \lambda_1 \]
- In water, it can be expressed as:
\[ v_2 = n_2 \lambda_2 \]
- Since \( n_1 = n_2 \), we can say:
\[ v_1 = n_1 \lambda_1 \quad \text{and} \quad v_2 = n_1 \lambda_2 \]
- This implies that:
\[ \lambda_1 \neq \lambda_2 \]
- Thus, the wavelength changes when the wave enters water.

**Hint**: Use the relationship \( v = n \lambda \) to understand how wavelength is affected by changes in velocity.

5. **Intensity Change**:
- Intensity is related to the square of the amplitude of the wave and the energy carried by the wave. When the wave enters a different medium, its intensity will also change due to the change in velocity and amplitude. Therefore, we have:
\[ I_1 \neq I_2 \]

**Hint**: Intensity is influenced by both amplitude and velocity, which can change when entering a new medium.

### Conclusion:
- The frequency remains constant (\( n_1 = n_2 \)).
- The velocity changes (\( v_1 \neq v_2 \)).
- The wavelength changes (\( \lambda_1 \neq \lambda_2 \)).
- The intensity changes (\( I_1 \neq I_2 \)).

### Summary of Key Points:
- **Frequency**: Constant across media.
- **Velocity**: Changes when entering a new medium.
- **Wavelength**: Changes due to the change in velocity.
- **Intensity**: Changes due to the change in amplitude and velocity.