(A) : The wave length of sound waves increases when they are refracted from air into water
(R): Velocity of sound is greater in water than in air

Options

A. Both 'A' and 'R' are true and 'R' is the correct, explanation of 'A'.
B. Both 'A' and 'R' are true and 'R' is not the correct explanation of 'A'
C. A' is true and 'R' is false
D. Both 'A' and 'R' are false

Answer

To solve the question, we need to analyze the statements (A) and (R) and determine their truthfulness and relationship.

### Step 1: Analyze Statement (A)
Statement (A) claims that "The wavelength of sound waves increases when they are refracted from air into water."

- When sound waves travel from air (less dense medium) into water (more dense medium), they undergo refraction.
- According to the principles of wave behavior, when sound waves enter a denser medium, their speed increases.
- The relationship between speed (c), wavelength (λ), and frequency (f) of a wave is given by the equation:
\[ c = f \cdot \lambda \]
- Since the frequency (f) remains constant when transitioning between media, if the speed (c) increases, the wavelength (λ) must also increase.

**Conclusion for Step 1:** Statement (A) is true.

### Step 2: Analyze Statement (R)
Statement (R) states that "Velocity of sound is greater in water than in air."

- The speed of sound in different media varies due to their densities and elastic properties.
- Sound travels faster in denser media, and water is denser than air.
- Therefore, the velocity of sound is indeed greater in water than in air.

**Conclusion for Step 2:** Statement (R) is true.

### Step 3: Determine the Relationship Between (A) and (R)
Now we need to determine if (R) is a correct explanation of (A).

- Since we established that the speed of sound increases when moving from air to water, and this increase in speed leads to an increase in wavelength (as per the equation \(c = f \cdot \lambda\)), we can conclude that (R) correctly explains (A).

### Final Conclusion
Both statements (A) and (R) are true, and (R) is the correct explanation of (A).

### Answer:
The correct option is: Both A and R are true, and R is the correct explanation of A.

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