Question

Transverse waves are generated in two uniform steel wires A and B by attaching their free ends to a fork of frequency 500 Hz. The diameter of wire A is half of B and tension in wire A is half the tension in wire B. What is the ratio of velocities of waves in A and B ?

• A. 1 : 2
• B. $\sqrt{2}:1$
• C. 2 : 1
• D. $1:\sqrt{2}$

Answer 1

The correct option is B $\sqrt{2}:1$

Since the same material is used in both the wires, the density of material is same.

Since the cross sectional area of the two wires is different, the mass per unit length would vary.

${\rho }_A={\rho }_B$
$⟹\frac{{\mu }_A}{A_A}=\frac{{\mu }_B}{A_B}$

It is given that diameter of A is half of that of B,

Hence $\frac{{\mu }_A}{A_A}=\frac{{\mu }_B}{4A_A}$

$⟹{\mu }_B=4{\mu }_A$

Also $T_B=2T_A$

Hence $\frac{v_A}{v_B}=\sqrt{\frac{T_A{\mu }_B}{T_B{\mu }_A}}$

$=\sqrt{2}$