A string is cut into three parts, having fundamental frequencies n1,n2,n3 respectively. Then original fundamental frequency n related by the expression as

Question

A string is cut into three parts, having fundamental frequencies n1,n2,n3 respectively. Then original fundamental frequency n related by the expression as (A) (1/n)=(1/n1)+(1/n2)+(1/n3) (B) n=n1× n2× n3 (C) n=n1+ n2+ n3 (D) n=(n1+ n2+ n3/3)

Tardigrade Admin · Accepted Answer

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

Q. A string is cut into three parts, having fundamental frequencies $n_{1}, n_{2}, n_{3}$ respectively. Then original fundamental frequency n related by the expression as

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

$n = n_{1} \times n_{2} \times n_{3}$

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

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

As $n \propto (1/ l)$ and $l = l_{1} + l_{2} + l_{3}$
$∴ \frac{1}{n} = \frac{1}{n _{1}} + \frac{1}{n _{2}} + \frac{1}{n _{3}}$ .

Q. A string is cut into three parts, having fundamental frequencies n1​,n2​,n3​ respectively. Then original fundamental frequency n related by the expression as

n1​=n1​1​+n2​1​+n3​1​

n=n1​×n2​×n3​

n=n1​+n2​+n3​

n=3n1​+n2​+n3​​

As n∝(1/l) and l=l1​+l2​+l3​ ∴n1​=n1​1​+n2​1​+n3​1​.