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Q.
If the tension and diameter of a sonometer wire of fundamental frequency $n$ is doubled and density is halved then its fundamental frequency will become
Waves
Solution:
Fundamental frequency $(n)=\frac{v}{2 l}$
or $n=\sqrt{\frac{T}{\mu}} \times \frac{1}{2 l}$ (i)
Tension becomes $ 2 T \ldots$ (ii)
$V=$ Ap per metre
or $v=\pi r^{2} \rho$
Now, $\mu^{\prime}=\pi(2 r)^{2} \frac{\rho}{2}$
or $\mu^{\prime}=2 \pi r^{2} \rho$
or $\mu^{\prime}=2 \mu$...(iii)
Putting (ii) and (iii) in equation (i),
$n^{\prime}=n$