(A): If in the presence of two independent audio signals, no beats are heard, it need not imply that they are of same frequency.
(R): If the frequency difference is more than 10 Hz no beats are heared.

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 analyze the given statements (A) and (R), we will break down the reasoning step by step.

### Step 1: Understanding Assertion (A)
Assertion (A) states: "If in the presence of two independent audio signals, no beats are heard, it need not imply that they are of the same frequency."

- **Explanation**: Beats occur when two sound waves of slightly different frequencies interfere with each other. The beat frequency is given by the absolute difference between the two frequencies. If the frequencies are the same, the beat frequency is zero, and thus no beats are heard. However, if the frequency difference is greater than a certain threshold (in this case, 10 Hz), the human ear may not perceive the beats, even though the frequencies are not the same.

### Step 2: Understanding Reason (R)
Reason (R) states: "If the frequency difference is more than 10 Hz, no beats are heard."

- **Explanation**: This statement is based on the threshold of human hearing. If the frequency difference between two audio signals exceeds 10 Hz, the time period of the beats becomes too short for the human ear to detect. The ear can typically perceive beats only when the frequency difference is less than about 10 Hz. Therefore, if the difference exceeds this threshold, the beats are not heard.

### Step 3: Evaluating the Truth of (A) and (R)
- **Assertion (A)** is **True**: It is indeed possible for two signals to have different frequencies and still not produce detectable beats if the frequency difference is large enough.
- **Reason (R)** is **True**: The statement that no beats are heard if the frequency difference is more than 10 Hz is accurate.

### Step 4: Conclusion
Since both (A) and (R) are true, but (R) does not provide a correct explanation for (A), we conclude that:
- Both (A) and (R) are true, but (R) is not the correct explanation of (A).

### Final Answer
Both (A) and (R) are true, and (R) is not the correct explanation of (A).

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