Transverse waves are generated in two uniform wires A and B of the. same material by attaching their free ends to a vibrating source of frequency 200Hz. The area of cross section of A is half that of B while tension on A is twice than on B. The ratio of wavelengths of transverse waves in A and B is

Question

Transverse waves are generated in two uniform wires A and B of the. same material by attaching their free ends to a vibrating source of frequency 200Hz. The area of cross section of A is half that of B while tension on A is twice than on B. The ratio of wavelengths of transverse waves in A and B is (A) 1:√2 (B) √2:1 (C) 1: 2 (D) 2: 1

Tardigrade Admin · Accepted Answer

(V1/V2) = √(T1/T2) × (A2 ρ2/A1 ρ1)

$1 : 2$

$2 : 1$

1 : 2

2 : 1

$\frac{V _{1}}{V _{2}} = \frac{T _{1}}{T _{2}} \times \frac{A _{2} ρ _{2}}{A _{1} ρ _{1}}$

1:2​

2​:1

1 : 2

2 : 1

V2​V1​​=T2​T1​​×A1​ρ1​A2​ρ2​​​

$1 : 2$

$2 : 1$

$\frac{V _{1}}{V _{2}} = \frac{T _{1}}{T _{2}} \times \frac{A _{2} ρ _{2}}{A _{1} ρ _{1}}$