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14.Waves and Sound
normal
Fundamental frequency of sonometer wire is $n$. If the length, tension and diameter of wire are tripled, the new fundamental frequency is
A
$\frac{n}{{\sqrt 3 }}$
B
$\frac{n}{{2\sqrt 3 }}$
C
$n \sqrt 3$
D
$\frac{n}{{3\sqrt 3 }}$
Solution
$\mathrm{n}=\frac{1}{2 l} \sqrt{\frac{\mathrm{T}}{\pi \mathrm{r}^{2} \rho}} $
$\Rightarrow \mathrm{n} \propto \frac{\sqrt{\mathrm{T}}}{l \mathrm{r}} $
$\Rightarrow \frac{\mathrm{n}_{1}}{\mathrm{n}_{2}}=\sqrt{\frac{\mathrm{T}_{1}}{\mathrm{T}_{2}}} \times \frac{l_{2}}{l_{1}} \times \frac{\mathrm{r}_{2}}{\mathrm{r}_{1}}$
$=\sqrt{\frac{\mathrm{T}}{3 \mathrm{T}}} \times \frac{3 l}{l} \times \frac{2 \mathrm{r}}{\mathrm{r}}=3 \sqrt{3}$
$ \Rightarrow \mathrm{n}_{2}=\frac{\mathrm{n}}{3 \sqrt{3}}$
Standard 11
Physics
