The laws of transverse vibrations of stretched strings are (i) the law of length (ii) law of tension and (iii) the law of mass.

(i) For a given wire tension (T) and linear density (m) are constant, the fundamental frequency of vibration (n) is inversely proportional to the vibrating length (l),

i.e. n ∞ 1/l

or, nl = constant.

(ii) For the length (l) and linear density (m) are constant, the fundamental frequency (n) is directly proportional to the square root of the tension (T),

i.e. n ∞ √T

or, n / √T = constant.

(iii) For the length (l) and tension (T) are constant, the fundamental frequency (n) varies inversely as the square root of the linear density (m),

i.e. n ∞ 1/√m

or, n √m = constant.