Question

Discuss the law of transverse vibrations in stretched strings.

Answer 1

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

1. The law of length:
   For a given wire with tension T (which is fixed) and mass per unit length µ (fixed) the frequency varies inversely with the vibrating length. Therefore,
   `"f" prop 1/l = "f" = "C"/l`
   

   ⇒ l × f = C, where C is a constant

2. The law of tension:
   For a given vibrating length l (fixed) and mass per unit length p, (fixed) the frequency varies directly with the square root of the tension T,
   f = `prop sqrt"T"`
   `=> "f" = "A"sqrt"T"`, where A is a constant
3. 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 µ,
   `"f" prop 1/sqrtmu`
   `=> "f" = "B"/sqrtmu`, where B is a constant