Question

how does tightening a string on a guitar affect its natural frequency?
the natural frequency stays the same
the natural frequency fluctuates
the natural frequency decreases
the natural frequency increases

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 string length, $T$ is the tension, and $\mu$ is the linear mass density. Tightening the string increases the tension $T$. Since frequency is directly proportional to the square root of tension, increasing tension raises the natural frequency.

Answer:

the natural frequency increases