Fundamental frequency of sonometer wire is n. If the length, tension and diameter of wire are tripled, the new fundamental frequency is

Question

Fundamental frequency of sonometer wire is n. If the length, tension and diameter of wire are tripled, the new fundamental frequency is (A) (n/√3) (B) (n/2 √3) (C) n √3 (D) (n/3 √3)

Tardigrade Admin · Accepted Answer

n=(1/2 l) √(T/π r2 ρ) ⇒ n propto (√T/l r) ⇒ (n1/n2)=√(T1/T2) × (l2/l1) × (r2/r1) =√(T/3 T) × (3 l/l) × (2 r/r)=3 √3 ⇒ n2=(n/3 √3)

Q. Fundamental frequency of sonometer wire is $n$ . If the length, tension and diameter of wire are tripled, the new fundamental frequency is

$\frac{n}{3}$

$\frac{n}{2 3}$

$n 3$

$\frac{n}{3 3}$

$n = \frac{1}{2 l} \frac{T}{π r ^{2} ρ}$
$\Rightarrow n \propto \frac{T}{l r}$
$\Rightarrow \frac{n _{1}}{n _{2}} = \frac{T _{1}}{T _{2}} \times \frac{l _{2}}{l _{1}} \times \frac{r _{2}}{r _{1}}$
$= \frac{T}{3 T} \times \frac{3 l}{l} \times \frac{2 r}{r} = 33$
$\Rightarrow n_{2} = \frac{n}{3 3}$

Q. Fundamental frequency of sonometer wire is n. If the length, tension and diameter of wire are tripled, the new fundamental frequency is

3​n​

23​n​

n3​

33​n​