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. 96 Hz
B. 192 Hz
C. 1200 Hz
D. 2400 Hz

Explanation

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

### Step-by-Step Solution:

1. **Understand the relationship between segments and frequency**:
The frequency of vibration is related to the number of segments (or harmonics) of the string. The relationship can be expressed as:
\[ f_n = n \cdot f_0 \]
where \( f_n \) is the frequency for \( n \) segments and \( f_0 \) is the fundamental frequency.

2. **Given information**:
- For 5 segments, the frequency \( f_5 = 480 \, \text{Hz} \).
- We need to find the frequency \( f_2 \) for 2 segments.

3. **Express \( f_5 \) in terms of \( f_0 \)**:
\[ f_5 = 5 \cdot f_0 \]
Substituting the known frequency:
\[ 480 = 5 \cdot f_0 \]

4. **Solve for the fundamental frequency \( f_0 \)**:
\[ f_0 = \frac{480}{5} = 96 \, \text{Hz} \]

5. **Now express \( f_2 \) in terms of \( f_0 \)**:
\[ f_2 = 2 \cdot f_0 \]

6. **Substitute the value of \( f_0 \)**:
\[ f_2 = 2 \cdot 96 = 192 \, \text{Hz} \]

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