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  4. A string of length 1 m fixed at both ends is vibrating in 3 text rd overtone. Tension in string is 200 N and linear mass density is 5 gm / m. Frequency of these vibrations is (in Hz ).

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Q. A string of length $1\,m$ fixed at both ends is vibrating in $3^{\text {rd }}$ overtone. Tension in string is $200\, N$ and linear mass density is $5\, gm / m$. Frequency of these vibrations is (in $Hz$ ).

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Solution:

$III ^{\text {rd }}$ overtone
$f=\frac{4 V}{2 L}=\frac{2 V}{L}=\frac{2}{1} \sqrt{\frac{200}{(5 / 1000)}}$
$=2(200) ; f=400 \,Hz$