Discuss the law of transverse vibrations In stretched string?

1.	Discuss the law of transverse vibrations In stretched string?
Answer» 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 p (fixed) the frequency varies inversely with the vibrating length. Therefore, f ∝ \(\frac{1}{l}\) ⇒ f = \(\frac{C}{2}\) ⇒1 × f = C, where C is constant (II) The law of tension: For a given vibrating length I (fixed) and mass per unit length p (fixed) the frequency varies directly with the square root of the tension T, f ∝ \(\sqrt T\) ⇒f = A\(\sqrt T\), Where A is constant (III) The law of mass: For a given vibrating length l (fixed) and tension T (fixed) the frequency varies inverely with the square root of the mass per unit length µ, f = \(\frac{1}{\sqrt μ}\) ⇒f = \(\frac{B}{\sqrt μ}\), Where B is constant

Answer»

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 p (fixed) the frequency varies inversely with the vibrating length.

Therefore,

f ∝ \(\frac{1}{l}\) ⇒ f = \(\frac{C}{2}\)

⇒1 × f = C, where C is constant

(II) The law of tension:

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

f ∝ \(\sqrt T\)

⇒f = A\(\sqrt T\), Where A is constant

(III) The law of mass:

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

Discussion