A string of length $1\ m$ fixed at both ends is vibrating in $3^{rd}$ overtone. Tension in string is $200\ N$ and linear mass density is $5\ gm/m$ . Frequency of these vibrations is ..... $Hz$
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$II{I^{rd}}$ overtone
$\mathrm{f}=\frac{4 \mathrm{V}}{2 \mathrm{L}}=\frac{2 \mathrm{V}}{\mathrm{L}}=\frac{2}{1} \sqrt{\frac{200}{(5 / 1000)}}=2(200)$
$\mathrm{f}=400 \mathrm{\,Hz}$
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