The frequency of tuning fork is 256 Hz. It will not resonate with a fork of frequency

Options

A. 768 Hz
B. 738 Hz
C. 512 Hz
D. 256 Hz

Explanation

To determine which frequency will not resonate with a tuning fork of frequency 256 Hz, we need to understand the concept of resonance in waves. Resonance occurs when two waves of the same frequency (or integer multiples of that frequency) overlap and reinforce each other.

### Step-by-Step Solution:

1. **Understanding Resonance**:
- Resonance occurs when the frequencies of two waves match or are integer multiples of each other. For a tuning fork of frequency \( f_1 = 256 \) Hz, it will resonate with frequencies \( f_2 \) that are equal to \( 256 \) Hz or multiples of \( 256 \) Hz (i.e., \( 512 \) Hz, \( 768 \) Hz, \( 1024 \) Hz, etc.).

2. **Identifying Resonant Frequencies**:
- The resonant frequencies can be expressed as:
\[ f_n = n \times 256 \text{ Hz} \]
where \( n \) is a positive integer (1, 2, 3, ...).

3. **Listing Possible Frequencies**:
- For \( n = 1 \): \( f_1 = 256 \) Hz
- For \( n = 2 \): \( f_2 = 512 \) Hz
- For \( n = 3 \): \( f_3 = 768 \) Hz
- For \( n = 4 \): \( f_4 = 1024 \) Hz
- And so on...

4. **Finding Non-Resonant Frequencies**:
- Any frequency that is not an integer multiple of \( 256 \) Hz will not resonate. For example, if we have a frequency of \( 300 \) Hz, it is not a multiple of \( 256 \) Hz.

5. **Conclusion**:
- Based on the above analysis, the frequency that will not resonate with a tuning fork of frequency \( 256 \) Hz is any frequency that does not fit the formula \( n \times 256 \) Hz.

### Final Answer:
The frequency of the tuning fork that will not resonate with \( 256 \) Hz is any frequency that is not \( 256 \) Hz or its integer multiples (like \( 512 \) Hz, \( 768 \) Hz, etc.).