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 superposed waves with frequencies of 6 Hz and 10 Hz, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Frequencies**:
- Let the frequency of the first wave (F1) be 6 Hz.
- Let the frequency of the second wave (F2) be 10 Hz.

2. **Understand Beat Frequency**:
- The beat frequency (Fb) is defined as the absolute difference between the frequencies of the two waves.
- Mathematically, it can be expressed as:
\[ Fb = |F2 - F1| \]

3. **Calculate the Beat Frequency**:
- Substitute the values of F1 and F2 into the formula:
\[ Fb = |10 \, \text{Hz} - 6 \, \text{Hz}| \]
- Perform the subtraction:
\[ Fb = |4 \, \text{Hz}| \]
- Since frequency is always a positive quantity, we can drop the absolute value:
\[ Fb = 4 \, \text{Hz} \]

4. **Conclusion**:
- The beat frequency produced by the superposition of the two waves is 4 Hz.

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

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