Question

A wire of length one meter under a certain initial tension emits a sound of fundamental frequency 256 Hz. When the tension is increased by 1 kg wt, the frequency of the frequency of the fundamental node increases to 320 Hz. The initial tension is

• A. 3/4 kg wt
• B. 4/3 kg wt
• C. 16/9 kg wt
• D. 20/9 kg wt

Answer 1

The correct option is C 16/9 kg wt

$f_i=256Hz$

Fundamental frequency

$L=\frac{\lambda }{2}$

$\lambda =2L$

$f=\frac{1}{2L}\sqrt{\frac{T}{\mu }}=256Hz$ (1)

When $T^{\prime }=T+1$

$f=\frac{1}{2L}\sqrt{\frac{T+1}{\mu }}=320Hz$ (2)

Dividing (1) by (2)

We get $\sqrt{\frac{T}{T+1}}=\frac{256}{320}$

$=\frac{T}{T+1}=\frac{65536}{102400}$

$=T=0.64(T+1)$

$=0.36T=0.64$

$=T=\frac{16}{9}$ Kg wt