Two waves of frequencies 6 Hz and 10 hz are superposed. The beat frequency produced is

Options

A. 6Hz
B. 10 Hz
C. 16 Hz
D. 4 Hz

Answer

To find the beat frequency produced by two waves of frequencies 6 Hz and 10 Hz, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Frequencies**:
We have two frequencies:
- \( f_1 = 6 \, \text{Hz} \)
- \( f_2 = 10 \, \text{Hz} \)

2. **Use the Beat Frequency Formula**:
The formula for calculating the beat frequency (\( f_{\text{beat}} \)) when two waves interfere is:
\[ f_{\text{beat}} = |f_1 - f_2| \]

3. **Substitute the Values**:
Now, we substitute the values of \( f_1 \) and \( f_2 \) into the formula:
\[ f_{\text{beat}} = |6 \, \text{Hz} - 10 \, \text{Hz}| \]

4. **Calculate the Difference**:
Calculate the difference:
\[ f_{\text{beat}} = |6 - 10| = |-4| = 4 \, \text{Hz} \]

5. **Conclusion**:
The beat frequency produced by the superposition of the two waves is:
\[ f_{\text{beat}} = 4 \, \text{Hz} \]

### Final Answer:
The beat frequency is **4 Hz**.

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