Laws of transverse vibrations in stretched strings

Laws of transverse vibrations in stretched strings

There are three laws of transverse vibrations of stretched strings which are given as follows:

(i)   The law of length :

For a given wire with tension T (which is fixed) and mass per unit length Î¼ (fixed) the frequency varies inversely with the vibrating length. Therefore,

⇒l×f = C, where C is a constant

(ii)   The law of tension:

For a given vibrating length l (fixed) and mass per unit length Î¼ (fixed) the frequency varies directly with the square root of the tension T,

(iii) The law of mass:

For a given vibrating length l (fixed) and tension T (fixed) the frequency varies inversely with the square root of the mass per unit length Î¼,