Beats are produced when two progressive waves of frequency 256 Hz and 260 Hz superpose. Then the resultant amplitude change periodically with frequency of

Answer

To solve the problem of determining the frequency of the resultant amplitude change when two progressive waves of frequencies 256 Hz and 260 Hz superpose, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Frequencies**:
- Let the frequency of the first wave, \( f_1 = 256 \, \text{Hz} \)
- Let the frequency of the second wave, \( f_2 = 260 \, \text{Hz} \)

2. **Calculate the Beat Frequency**:
- The beat frequency is determined by the difference between the two frequencies:
\[ f_{\text{beat}} = |f_2 - f_1| \]
- Substituting the values:
\[ f_{\text{beat}} = |260 \, \text{Hz} - 256 \, \text{Hz}| = |4 \, \text{Hz}| \]
- Therefore, the beat frequency is \( 4 \, \text{Hz} \).

3. **Conclusion**:
- The resultant amplitude of the superposed waves changes periodically with a frequency of \( 4 \, \text{Hz} \).

### Final Answer:
The resultant amplitude changes periodically with a frequency of **4 Hz**.

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