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(D) For a string fixed at both ends,the frequency of the $n^{th}$ harmonic is given by $f_n = \frac{n v}{2L}$,where $n = 1, 2, 3, \dots$ and $v = \sqr

Vedclass · Accepted Answer

$400$

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(D) For a string fixed at both ends,the frequency of the $n^{th}$ harmonic is given by $f_n = \frac{n v}{2L}$,where $n = 1, 2, 3, \dots$ and $v = \sqrt{\frac{T}{\mu}}$.The $3^{rd}$ overtone corresponds to the $4^{th}$ harmonic,so $n = 4$.Given: Length $L = 1 \, m$,Tension $T = 200 \, N$,Linear mass density $\mu = 5 \, g/m = 5 	imes 10^{-3} \, kg/m$.First,calculate the wave speed $v = \sqrt{\frac{200}{5 	imes 10^{-3}}} = \sqrt{40000} = 200 \, m/s$.Now,calculate the frequency $f_4 = \frac{4 	imes 200}{2 	imes 1} = 2 	imes 200 = 400 \, Hz$.

$A$ string of length $1 \, m$ fixed at both ends is vibrating in the $3^{rd}$ overtone. The tension in the string is $200 \, N$ and the linear mass density is $5 \, g/m$. The frequency of these vibrations is ..... $Hz$.

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