1. Tardigrade
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  4. A piano wire having a diameter of 0.60 mm is replaced by another wire of same material but with a diameter of 0.62 mm. If the tension of the wire is kept the same, then the percentage change in the frequency of the fundamental tone is %.

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Q. A piano wire having a diameter of $0.60\, mm$ is replaced by another wire of same material but with a diameter of $0.62\, mm$. If the tension of the wire is kept the same, then the percentage change in the frequency of the fundamental tone is______$\%$.

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Solution:

$v=\frac{1}{ Dl } \sqrt{\frac{ T }{\pi d }}$
$\Rightarrow v \propto \frac{1}{ D }$
$\Rightarrow \frac{v'}{v}=\frac{ D }{ D'}$
$\Rightarrow\left(\frac{v'}{v}-1\right) \times 100=\left(\frac{ D }{ D'}-1\right) \times 100$
$=\left(\frac{0.60}{0.62}-1\right) \times 100$
$=-\frac{100}{31}=-3.2 \%$