Question

how can you make the natural frequency of a string increase?

decrease the tension of the string

loosen the string

cut the string

tighten the string

Explanation:

The natural frequency of a vibrating string is given by the formula $f = \frac{1}{2L}\sqrt{\frac{T}{\mu}}$, where $L$ is the length of the string, $T$ is the tension, and $\mu$ is the linear mass density. To increase the frequency, we can increase tension, decrease length, or decrease linear mass density.

• Decreasing tension or loosening the string reduces $T$, lowering frequency.
• Cutting the string reduces $L$, which increases frequency, but tightening the string directly increases $T$, which also increases frequency. However, tightening is a direct, common method to raise a string's natural frequency, and both cutting and tightening work, but in standard context, tightening is the primary intended answer here as it's a controllable adjustment for frequency change in stringed instruments.

Answer:

cut the string, tighten the string