Question

A wire of length one metre 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 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

Answer: (C)

Let tension be $T$
$f_{1}=\sqrt{\frac{T}{\mu}} \times \frac{1}{2 l}=256 \ldots$ (i)
$f_{2}=\sqrt{\frac{T+10}{\mu}} \times \frac{1}{2 l}=320 \ldots$ (ii)
$ \sqrt{\frac{T}{T+10}}=\frac{256}{320}$ [Dividing (i) by (ii)]
or $\frac{T}{T+10}=\frac{(16)^{2}}{(16)^{2} \times(20)^{2}}$
or $\frac{T}{T+10}=\frac{16^{2}}{(20)^{2}}$
or $400 T=256 T^{2}+2560$
or $144 T=2560$
or $T=\frac{2560}{144}$
or $T=\frac{2560}{16 \times 9}$
or $T=\frac{160}{9}$ Newton
$=\frac{16}{9} kg - wt$