A string of length $1 m$ fixed at both ends is vibrating in $3^{r d}$ overtone. Tension in string is $200 N$ and linear mass denstiy is $5 g m / m$ . Frequency of these vibrations is (in $H z$ ).

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Solution

Given, length of the string, $L = 1 m$
Tension in the string, $T = 200 N$
Linear mass density,
$μ = 5 g m / m = 5 \times 10^{- 3} k g / m$

For $3^{r d}$ overtone of $4^{t h}$ harmonic,
$f = \frac{4}{2 L} \sqrt{\frac{T}{μ}}$
$f = \frac{4}{2 \times 1} \sqrt{\frac{200}{(5 \times 10^{- 3}}} = 2 (200)$
$f = 400 H z$

Final answer: (400)

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