A string vibrates in 5 segments to a frequency of 480 Hz. The frequency that will cause it to vibrate in 2 segments will be

Options

A. (a) 96 Hz
B. (b) 192 Hz
C. (c) 1200 Hz
D. (d) 2400 Hz

Explanation

To solve the problem, we need to find the frequency that causes the string to vibrate in 2 segments, given that it vibrates in 5 segments at a frequency of 480 Hz.

### Step-by-Step Solution:

1. **Identify the Harmonics**:
- The string vibrating in 5 segments corresponds to the 5th harmonic (f5).
- The frequency given for the 5th harmonic is 480 Hz.

2. **Relate Harmonics to Fundamental Frequency**:
- The relationship between the harmonics and the fundamental frequency (f0) can be expressed as:
- \( f_n = n \cdot f_0 \)
- For the 5th harmonic:
- \( f_5 = 5 \cdot f_0 \)
- Therefore, we can write:
- \( 480 \, \text{Hz} = 5 \cdot f_0 \)

3. **Calculate the Fundamental Frequency (f0)**:
- Rearranging the equation gives:
- \( f_0 = \frac{480 \, \text{Hz}}{5} = 96 \, \text{Hz} \)

4. **Find the Frequency for 2 Segments (f2)**:
- The frequency for the 2nd harmonic (f2) is given by:
- \( f_2 = 2 \cdot f_0 \)
- Substituting the value of f0 we found:
- \( f_2 = 2 \cdot 96 \, \text{Hz} = 192 \, \text{Hz} \)

5. **Conclusion**:
- The frequency that will cause the string to vibrate in 2 segments is **192 Hz**.

### Final Answer:
The frequency that will cause the string to vibrate in 2 segments is **192 Hz**.

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