What is the relationship between the frequency of a vibrating stretched string and its length? - Leaving Cert Physics - Question c - 2008

The frequency of a vibrating stretched string is inversely proportional to its length. This means that as the length of the string increases, its frequency decreases, and vice versa. The relationship can be expressed mathematically as:

$f imes L = k$

where:

• $f$ is the frequency of the vibrating string,
• $L$ is the length of the string,
• $k$ is a constant dependent on factors such as tension and mass per unit length of the string.

Thus, we can summarize this relationship as:

$f \propto \frac{1}{L}$