To decrease the fundamental frequency of a stretched string fixed at both ends one might

Options

A. increase its tension
B. increase its wave velocity
C. increase its length
D. decrease its linear mass density

Explanation

To decrease the fundamental frequency of a stretched string fixed at both ends, one might consider the following steps:

### Step-by-Step Solution:

1. **Understand the Fundamental Frequency Formula**: The fundamental frequency \( f \) of a stretched string fixed at both ends is given by the formula:
\[ f = \frac{1}{2L} \sqrt{\frac{T}{\mu}} \]
where:
- \( L \) = length of the string,
- \( T \) = tension in the string,
- \( \mu \) = linear mass density of the string (mass per unit length).

2. **Identify Factors Affecting Frequency**: From the formula, we can see that the fundamental frequency is inversely proportional to the length \( L \) and directly proportional to the square root of the tension \( T \) and inversely proportional to the square root of the linear mass density \( \mu \).

3. **Decrease the Frequency**: To decrease the fundamental frequency \( f \), we can:
- **Increase the Length \( L \)**: By increasing the length of the string, the frequency will decrease since \( f \) is inversely proportional to \( L \).
- **Decrease the Tension \( T \)**: Reducing the tension in the string will also lead to a decrease in frequency since \( f \) is directly proportional to the square root of \( T \).
- **Increase the Linear Mass Density \( \mu \)**: Increasing the mass per unit length of the string will also result in a lower frequency since \( f \) is inversely proportional to the square root of \( \mu \).

4. **Conclusion**: Therefore, to decrease the fundamental frequency of a stretched string fixed at both ends, one might:
- Increase the length of the string,
- Decrease the tension in the string,
- Increase the mass of the string (or use a thicker string).