(A): The maximum number of beats that the human ear can detect is "10''
(R): The time of persistence of hearing is '0.1' sec.

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) provided:

1. **Statement (A)**: The maximum number of beats that the human ear can detect is "10".
2. **Statement (R)**: The time of persistence of hearing is '0.1' sec.

We need to determine if statement (A) is true and if statement (R) is true, and also whether (R) is the correct explanation for (A).

### Step 1: Understanding Beats
Beats occur when two sound waves of slightly different frequencies interfere with each other. The frequency of beats (f_beat) is given by the formula:
\[ f_{beat} = |f_1 - f_2| \]
where \( f_1 \) and \( f_2 \) are the frequencies of the two waves.

### Step 2: Maximum Beats Detection
The maximum number of beats that can be detected by the human ear is related to the time of persistence of hearing. The human ear can typically detect a maximum of around 10 beats per second. This is because if the beats occur faster than this, the ear cannot distinguish between them due to the persistence of hearing.

### Step 3: Persistence of Hearing
The time of persistence of hearing is the duration for which the ear retains the perception of a sound after it has stopped. A typical value for this is around 0.1 seconds. This means that if the beats occur more frequently than 10 beats per second, the ear will not be able to distinguish them clearly.

### Step 4: Evaluating Statements
- **Evaluating (A)**: The statement that the maximum number of beats that the human ear can detect is "10" is true.
- **Evaluating (R)**: The statement that the time of persistence of hearing is '0.1' sec is also true.

### Step 5: Relationship Between (A) and (R)
Since the maximum number of beats detectable (10 beats per second) is directly related to the time of persistence of hearing (0.1 seconds), we can conclude that (R) is a correct explanation for (A).

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