A sound waves passes from a medium `A` to a medium `B`. The velocity of sound in `B` is greater than 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

Explanation

To solve the problem step by step, we will analyze the behavior of sound waves as they transition from medium A to medium B, considering the properties of sound waves and the implications of the given conditions.

### Step 1: Understand the properties of sound waves in different media
- Sound waves travel at different velocities in different media. Here, we know that the velocity of sound in medium B (VB) is greater than in medium A (VA).
- This difference in velocity suggests that medium A is denser than medium B.

**Hint:** Remember that the speed of sound is influenced by the medium's density and elasticity.

### Step 2: Analyze the transmission of sound waves
- Since there is no absorption or reflection at the boundary, the sound wave will transmit from medium A to medium B without losing energy.
- The amplitude of the transmitted wave can be calculated using the formula:
\[ A_{transmitted} = \frac{2 \cdot v_B}{v_B + v_A} \cdot A_{incident} \]
- This indicates that the amplitude of the transmitted wave will depend on the velocities of the sound in both media.

**Hint:** The amplitude of the transmitted wave is affected by the velocities of sound in both media.

### Step 3: Frequency of the sound wave
- The frequency of the sound wave remains constant as it transitions from one medium to another. This is because frequency is determined by the source of the sound and does not change when the wave moves between media.
- Therefore, \( f_{incident} = f_{transmitted} \).

**Hint:** Frequency is a property of the source and does not change during transmission between media.

### Step 4: Relationship between velocity, frequency, and wavelength
- The relationship between velocity (v), frequency (f), and wavelength (λ) is given by the equation:
\[ v = f \cdot \lambda \]
- Since the frequency remains constant and the velocity in medium B is greater than in medium A, we can conclude that the wavelength in medium B must be greater than in medium A.

**Hint:** If the velocity increases while frequency remains constant, the wavelength must also increase.

### Step 5: Intensity of the sound wave
- Intensity (I) is defined as the power per unit area, and since there is no absorption or reflection, the intensity of the sound wave remains constant as it passes from medium A to medium B.
- This means that the intensity of the incident wave is equal to the intensity of the transmitted wave.

**Hint:** Intensity remains constant when there is no energy loss due to absorption or reflection.

### Conclusion
Based on the analysis, we can summarize the outcomes:
1. The amplitude of the transmitted wave changes according to the velocities of the media.
2. The frequency of the sound wave remains constant.
3. The wavelength increases as the sound wave moves from medium A to medium B.
4. The intensity of the sound wave remains unchanged.

Thus, the correct options are 1, 2, and 4.