If n1, n2 and n3 are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is given by

Question

If n1, n2 and n3 are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is given by (A) (1/n)=(1/n1)+(1/n2)+(1/n3) (B) (1/√n)=(1/√n1)+(1/√n2)+(1/√n3) (C) √n=√n1+√n2+√n3 (D) n=n1+n2+n3

Tardigrade Admin · Accepted Answer

As n propto (1/l) or l propto (1/n) and l =l1+l2+l3 ⇒ (1/n)=(1/n1)+(1/n2)+(1/n3)

Q. If $n_{1}, n_{2}$ and $n_{3}$ are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency $n$ of the string is given by

$\frac{1}{n} = \frac{1}{n _{1}} + \frac{1}{n _{2}} + \frac{1}{n _{3}}$

$\frac{1}{n} = \frac{1}{n _{1}} + \frac{1}{n _{2}} + \frac{1}{n _{3}}$

$n = n_{1} + n_{2} + n_{3}$

$n = n_{1} + n_{2} + n_{3}$

As $n \propto \frac{1}{l}$ or $l \propto \frac{1}{n}$
and $l = l_{1} + l_{2} + l_{3}$
$\Rightarrow \frac{1}{n} = \frac{1}{n _{1}} + \frac{1}{n _{2}} + \frac{1}{n _{3}}$

Q. If n1​,n2​ and n3​ are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is given by

n1​=n1​1​+n2​1​+n3​1​

n​1​=n1​​1​+n2​​1​+n3​​1​

n​=n1​​+n2​​+n3​​

n=n1​+n2​+n3​

As n∝l1​ or l∝n1​ and l=l1​+l2​+l3​ ⇒n1​=n1​1​+n2​1​+n3​1​

Q. If $n_{1}, n_{2}$ and $n_{3}$ are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency $n$ of the string is given by

$\frac{1}{n} = \frac{1}{n _{1}} + \frac{1}{n _{2}} + \frac{1}{n _{3}}$

$\frac{1}{n} = \frac{1}{n _{1}} + \frac{1}{n _{2}} + \frac{1}{n _{3}}$

$n = n_{1} + n_{2} + n_{3}$

$n = n_{1} + n_{2} + n_{3}$

As $n \propto \frac{1}{l}$ or $l \propto \frac{1}{n}$
and $l = l_{1} + l_{2} + l_{3}$
$\Rightarrow \frac{1}{n} = \frac{1}{n _{1}} + \frac{1}{n _{2}} + \frac{1}{n _{3}}$