A sound wave passes from a medium A to a medium B. The velocity of sound B is greater than that in A. Assume that there is no absorption or reflection at the boundary. As the wave moves across the boundary

Options

A. the frequency of sound will not change
B. the wavelength will increase
C. the wavelength will decrease
D. the intensity of sound will not change

Answer

To solve the problem of how a sound wave behaves as it passes from medium A to medium B, where the velocity of sound in medium B is greater than in medium A, we can analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding the Parameters**:
- Let the velocity of sound in medium A be \( V_A \) and in medium B be \( V_B \).
- Given that \( V_B > V_A \).
- The frequency of the sound wave is denoted as \( f \).
- The wavelength in medium A is \( \lambda_A \) and in medium B is \( \lambda_B \).

2. **Frequency of the Sound Wave**:
- The frequency of a sound wave is determined by the source of the sound and does not change when the wave moves from one medium to another.
- Therefore, \( f_A = f_B = f \).
- **Conclusion**: The frequency remains constant as the wave crosses the boundary.

3. **Relationship Between Velocity, Wavelength, and Frequency**:
- The relationship between velocity, wavelength, and frequency is given by the equation:
\[ V = f \cdot \lambda \]
- For medium A:
\[ V_A = f \cdot \lambda_A \]
- For medium B:
\[ V_B = f \cdot \lambda_B \]

4. **Comparing Velocities**:
- Since \( V_B > V_A \) and \( f \) is constant, we can compare the two equations:
\[ f \cdot \lambda_B > f \cdot \lambda_A \]
- Dividing both sides by \( f \) (since \( f \) is positive), we get:
\[ \lambda_B > \lambda_A \]
- **Conclusion**: The wavelength increases as the wave moves from medium A to medium B.

5. **Intensity of the Sound Wave**:
- The intensity \( I \) of a sound wave is given by:
\[ I \propto A^2 \cdot f^2 \cdot \frac{P}{V} \]
where \( A \) is the amplitude, \( P \) is the pressure, and \( V \) is the velocity of sound in the medium.
- As the wave travels from medium A to medium B, the velocity changes, which will affect the intensity.
- Since \( V_B > V_A \), the intensity will change as well.
- **Conclusion**: The intensity of the sound wave will change when crossing the boundary.

### Final Answers:
- The frequency of the sound wave does not change (Correct).
- The wavelength of the sound wave increases (Correct).
- The intensity of the sound wave will change (Incorrect).

### Summary of Correct Options:
- The correct options are:
1. The frequency of the sound will not change.
2. The wavelength will increase.