During superposition of two waves of nearly equal frequencies , beat frequency is defined as the

Options

A. Sum of frequencies of interfering waves
B. Number of times the resultant intensity becomes maximum or minimum is one second
C. Average of frequencies of interfering waves
D. Number of times the resultant amplitude becomes maximum or minimum in one second .

Answer

To solve the question regarding the definition of beat frequency during the superposition of two waves of nearly equal frequencies, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Wave Superposition**:
- When two waves of nearly equal frequencies interfere, they can create a phenomenon known as beats. This occurs due to the constructive and destructive interference of the waves.

2. **Defining the Waves**:
- Let the two waves be represented as:
- \( y_1 = A \sin(\omega_1 t) \)
- \( y_2 = A \sin(\omega_2 t) \)
- Here, \( A \) is the amplitude, \( \omega_1 \) and \( \omega_2 \) are the angular frequencies of the waves.

3. **Condition for Beat Frequency**:
- The condition for beat frequency arises when the difference between the two frequencies is small, i.e., \( |\omega_1 - \omega_2| \) is small.

4. **Calculating Beat Frequency**:
- The beat frequency \( f_b \) can be defined as:
\[ f_b = |\omega_1 - \omega_2| \]
- This indicates how many times the resultant amplitude reaches its maximum and minimum values in one second.

5. **Interpreting the Beat Frequency**:
- The beat frequency represents the frequency at which the amplitude of the resultant wave oscillates between maximum and minimum values.

6. **Choosing the Correct Definition**:
- Among the options provided, the correct definition of beat frequency is:
- The number of times the resultant amplitude becomes maximum or minimum in one second, which corresponds to option 4.

### Conclusion:
The beat frequency during the superposition of two waves of nearly equal frequencies is defined as the number of times the resultant amplitude becomes maximum or minimum in one second, mathematically represented as \( |\omega_1 - \omega_2| \).