State and explain the laws of vibrations of stretched strings.

Explanation

The fundamental frequency of vibration of a stretched string or wire is given by
`n=(1)/(2L)sqrt((T)/(m))` where L is the vibrating length, m the mass per unit length of the string and T the tension in the string. From the above expression, we can state the following three laws of vibrating strings :
(1) Law of length : The fundamental frequency of vibrations of a streched string is invessely proportional to its vibrating length, if the tension and mass per unit length are kept constant.
(2) Law of tension : The fundamental frequency of vibrations of a stretched string is direactly proportional to the square root of the applied tension, if the length and mass per unit length are kept constant.
(3) Law of mass : The fundamental frequency of vibrations of a stretched is inversely proportional to the square root of its mass per unit length, if the length and tension are kept constant.