The fundamental frequency of a sonometer wire of length l is f0. A bridge is now introduced at a distance of Δ l from the center of the wire (Δ l

Question

The fundamental frequency of a sonometer wire of length l is f0. A bridge is now introduced at a distance of Δ l from the center of the wire (Δ l < < l) . The number of beats heard if both sides of the bridges are set into vibration in their fundamental modes are (A) (8 f0 Δ l/l) (B) (f0 Δ l/l) (C) (2 f0 Δ l/l) (D) (4 f0 Δ l/l)

Tardigrade Admin · Accepted Answer

f0=(1/2 L) √(T/μ), f=(1/2 L) √(T/μ) ⇒ Δ f=2 f (Δ l/l prime) ⇒ Δ f=2 f0 ((2 Δ l)/l / 2) =8 ((f0 Δ l)/l)

Q. The fundamental frequency of a sonometer wire of length $l$ is $f_{0}$ . A bridge is now introduced at a distance of $Δ l$ from the center of the wire $(Δ l << l) .$ The number of beats heard if both sides of the bridges are set into vibration in their fundamental modes are

$\frac{8 f _{0} Δ l}{l}$

$\frac{f _{0} Δ l}{l}$

$\frac{2 f _{0} Δ l}{l}$

$\frac{4 f _{0} Δ l}{l}$

$f_{0} = \frac{1}{2 L} \frac{T}{μ},$
$f = \frac{1}{2 L} \frac{T}{μ}$
$\Rightarrow Δ f = 2 f \frac{Δ l}{l ^{'}}$
$\Rightarrow Δ f = 2 f_{0} \frac{( 2Δ l )}{l /2}$
$= 8 \frac{( f _{0} Δ l )}{l}$

Q. The fundamental frequency of a sonometer wire of length l is f0​. A bridge is now introduced at a distance of Δl from the center of the wire (Δl<<l). The number of beats heard if both sides of the bridges are set into vibration in their fundamental modes are

l8f0​Δl​

lf0​Δl​

l2f0​Δl​

l4f0​Δl​