Two vibrating strings of same length, same cross section area and stretched to same tension is made of materials with densities ρ and 2 ρ. Each string is fixed at both ends. If v 1 represents the fundamental mode of vibration of the one made with density ρ and v2 for another, then v1 / v2 is:

Question

Two vibrating strings of same length, same cross section area and stretched to same tension is made of materials with densities ρ and 2 ρ. Each string is fixed at both ends. If v 1 represents the fundamental mode of vibration of the one made with density ρ and v2 for another, then v1 / v2 is: (A) (1/2) (B) 2 (C) √2 (D) (1/√2)

Tardigrade Admin · Accepted Answer

Velocity of sound is inversely proportional to the square root of density of the medium. i.e., V ⋅ ρ= constant ⇒ (V1/V2)=√(ρ2/ρ1) =√(2 ρ/ρ)=√2

$\frac{1}{2}$

2

$2$

$\frac{1}{2}$

Velocity of sound is inversely proportional to the square root of density of the medium.
i.e., $V \cdot ρ =$ constant
$\Rightarrow \frac{V _{1}}{V _{2}} = \frac{ρ _{2}}{ρ _{1}}$
$= \frac{2 ρ}{ρ} = 2$

21​

2

2​

2​1​

Velocity of sound is inversely proportional to the square root of density of the medium. i.e., V⋅ρ= constant ⇒V2​V1​​=ρ1​ρ2​​​ =ρ2ρ​​=2​

$\frac{1}{2}$

$2$

$\frac{1}{2}$

Velocity of sound is inversely proportional to the square root of density of the medium.
i.e., $V \cdot ρ =$ constant
$\Rightarrow \frac{V _{1}}{V _{2}} = \frac{ρ _{2}}{ρ _{1}}$
$= \frac{2 ρ}{ρ} = 2$