Question

How is the frequency of a stretched string related to its length?

Answer 1

1. The stretched string produces transverse waves.
2. The frequency of these waves is determined by the tension and length of the stretched string.
3. In a stretched string, the frequency of transverse waves is given by,
   $f=\frac{n}{2L}\sqrt{\frac{T}{\mu }}$
   Where $f$ is the frequency, $L$ is the length of the string, $T$ is the tension of the string, $\mu$mass per unit length.
4. Frequency is inversely proportional to the length of the string.
   As we can easily say that,

$f\propto \frac{1}{L}$
Therefore, the frequency of the stretched wire is inversely proportional to the length as the length increases, the frequency will decrease.