Question

What are the factors that affect the frequency of a vibrating string and how do they affect the frequency?

Answer 1

The frequency (f) of a vibrating string is affected by:
(i) The length of the vibrating string. Frequency is inversely proportional to the length, i.e, `"f"α1/"l"`. it means, if length increases, frequency becomes less and if length decreases, frequency increases.
(ii) It is directly proportional to the square root of the tension, other factors remaining the same, e.g., if tension (or stretching force) is made 4 times, then the frequency will be `(sqrt4=2)` doubled.
(iii) The frequency, (f) is inversely proportional to the square root of the mass of unit length of the vibrating string, i.e., `"f"α1/sqrt"m′"` if m' is the mass of unit length of the string. Since m' = πr².l, it shows that f is `α1/sqrt("r"^2)` or `1/"r"`, where r is the radius of the vibrating strings.