A stretched string is vibrating in the second | vedclass

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(A) For a stretched string fixed at both ends,the frequency of the $ n $-th overtone is given by $ f_n = (n+1) f_1 $,where $ f_1 $ is the fundamental

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$ 4 $ and $ 3 $

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(A) For a stretched string fixed at both ends,the frequency of the $ n $-th overtone is given by $ f_n = (n+1) f_1 $,where $ f_1 $ is the fundamental frequency. For the second overtone,$ n = 2 $,so the string vibrates in the $ 3^{rd} $ harmonic mode. In the $ 3^{rd} $ harmonic mode,the string has $ 3 $ loops. The number of nodes $( N )$ in a standing wave with $ p $ loops is $ p+1 $. Here,$ p = 3 $,so the number of nodes is $ 3+1 = 4 $. The number of antinodes $( A )$ is equal to the number of loops,which is $ 3 $. Therefore,there are $ 4 $ nodes and $ 3 $ antinodes.

$A$ stretched string is vibrating in the second overtone. The number of nodes and antinodes between the ends of the string are respectively:

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