Question
Find the frequency of note emitted by a string of length $10\sqrt{10}\text{cm},$ under tension of 3.14kg. Radius of string is 0.5mm and density = 9.8g/cc.
✓
Answer
Here $\text{l}=10\sqrt{10}\text{cm}=0.1\sqrt{10}\text{m}$
$\text{T}=3.14\text{kg wt}=3.14\times9.8\text{N}$
$\text{D}=2\text{r}=2\times0.5\text{mm}$
$=1\text{mm}=0.001\text{m}$
$\rho=9.8\text{g/cc}=9.8\times10^3\text{kg/m}^3$
As $\text{V}=\frac{1}{\text{lD}}\sqrt{\frac{\text{T}}{\pi\rho}}$
$\text{V}=100\text{Hz}$
$\text{T}=3.14\text{kg wt}=3.14\times9.8\text{N}$
$\text{D}=2\text{r}=2\times0.5\text{mm}$
$=1\text{mm}=0.001\text{m}$
$\rho=9.8\text{g/cc}=9.8\times10^3\text{kg/m}^3$
As $\text{V}=\frac{1}{\text{lD}}\sqrt{\frac{\text{T}}{\pi\rho}}$
$\text{V}=100\text{Hz}$
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