Question

if anyone into an entry at the fundamental frequencies of three segments into which a string is divided than the original fundamental frequency and of the string is given by ?
write the steps of solution..​

Answer 1

1 over straight n space equals space 1 over n subscript 1 plus 1 over n subscript 2 plus 1 over n subscript 3

For first part, n1 = fraction numerator straight v over denominator 2 straight l subscript 1 end fraction space rightwards double arrow space l subscript 1 space equals space fraction numerator v over denominator 2 n subscript 1 end fraction

For second part, n2 = fraction numerator straight v over denominator 2 straight l subscript 2 end fraction space rightwards double arrow space l subscript 2 space equals space fraction numerator v over denominator 2 n subscript 2 end fraction

For third part, n3 = fraction numerator straight v over denominator 2 straight l subscript 3 end fraction space rightwards double arrow space l subscript 3 space equals space fraction numerator v over denominator 2 n subscript 3 end fraction

For the complete wire,

straight n space equals space fraction numerator straight v over denominator 2 straight l end fraction space rightwards double arrow space straight l space equals space fraction numerator straight v over denominator 2 straight n end fraction

We have, l = l1 + l2 + l3

That is,

fraction numerator straight v over denominator 2 straight n end fraction space equals space fraction numerator v over denominator 2 n subscript 1 end fraction space plus space fraction numerator v over denominator 2 n subscript 2 end fraction plus fraction numerator v over denominator 2 n subscript 3 end fraction

space 1 over n space equals space 1 over n subscript 1 space plus space 1 over n subscript 2 plus 1 over n subscript 3

For first part, n1 = fraction numerator straight v over denominator 2 straight l subscript 1 end fraction space rightwards double arrow space l subscript 1 space equals space fraction numerator v over denominator 2 n subscript 1 end fraction

For second part, n2 = fraction numerator straight v over denominator 2 straight l subscript 2 end fraction space rightwards double arrow space l subscript 2 space equals space fraction numerator v over denominator 2 n subscript 2 end fraction

For third part, n3 = fraction numerator straight v over denominator 2 straight l subscript 3 end fraction space rightwards double arrow space l subscript 3 space equals space fraction numerator v over denominator 2 n subscript 3 end fraction

For the complete wire,

straight n space equals space fraction numerator straight v over denominator 2 straight l end fraction space rightwards double arrow space straight l space equals space fraction numerator straight v over denominator 2 straight n end fraction

We have, l = l1 + l2 + l3

That is,