Vibrations Produced in a String

Standing waves are formed on a string fixed at both ends when plucked at the centre, such that a node is formed at rigid ends and an antinode is formed in between them — this phenomenon is called vibrations produced in a string.

It states that the vibrations of a string is inversely proportional to the length of the vibrating string when tension (T) and mass per unit length (m) are constants.

It states that the fundamental frequency of vibration of a string is directly proportional to the square root of tension, when length (l) and mass per unit length (m) are constants.

It states that the fundamental frequency of vibrations of a stretched string is inversely proportional to the square root of mass per unit length, when tension (T) and length (l) are constants.

n ∝ \[\frac {1}{\sqrt m}\]​​(T and l constant)

Also expressed as: n ∝ \[\frac {1}{\sqrt ρ}\]​ ​n ∝ \[\frac {1}{r}\]