A string with a mass density of 4×10^{-3}, kg/m is under tension of 360, N and is fixed at both end

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14.Waves and Sound

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A string with a mass density of $4\times10^{-3}\, kg/m$ is under tension of $360\, N$ and is fixed at both ends. One of its resonance frequencies is $375\, Hz$. The next higher resonance frequency is $450\, Hz$. The mass of the string is

A

$2\times10^{-3}\, kg$

B

$3\times10^{-3}\, kg$

C

$4\times10^{-3}\, kg$

D

$8\times10^{-3}\, kg$

Solution

$\mathrm{f}_{1}=\frac{1}{2 \ell} \sqrt{\frac{\mathrm{T}}{\mu}}=450-375=75$

$\ell=\frac{1}{2 \times 75} \times \sqrt{\frac{360}{4 \times 10^{-3}}}=\frac{300}{150}=2 \mathrm{\,m}$

$\mathrm{m}=\mu \times 2=8 \times 10^{-3} \mathrm{\,kg}$

Standard 11

Physics

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