Answer to Question #164202 in Optics for Yolande

Question

(i.) The velocity v of a transverse wave on a stretched string is given by V = sqrt(T/µ) where T is the tension and µ is the mass per unit length.

      (a.) Show that the equation is dimensionally correct.

      (b.) Derive an expression for the fundamental frequency of a vibrating wire.

Answer 1

Answer

a) for dimensionally correct both side must be equal

In left hand side

Velocity= m/sec

In right hand side

$\sqrt{\frac{T}{\mu}}=\sqrt{\frac{kg .meter.meter}{sec^2.kg.}}=m/sec$

Both side are equal so hence proved.

b) In the fundamental mode of vibration of the string, there will be an antinode in between the two nodes a the fixed points.If l is the length of the string then

$\lambda=2l$

Frequency is given

$f=\frac{v}{\lambda}=\frac{v}{2l}=\frac{1}{2l}(\sqrt\frac{T}{\mu})$