Question

Two string $A$ and $B,$ made of same material, are stretched by same tension. The radius of string $A$ is double of the radius of $B.$ $A$ transverse wave travels on $A$ with speed $v_A$ and on $B$ with speed $v_B.$ The ratio $v_A/v_B$ is

• A. $1/2$
• B. $2$
• C. $1/4$
• D. $4$

Answer 1

Answer: (A)

$1/2$

As we know, speed of transverse wave $V=\sqrt{\frac{T}{M}}$,

where T= Tension

$H=$ mass per unit length of string.

$M=\frac{m}{L},m=\mathrm{mass}$

$1=\mathrm{leng}th$

On $M=5\cdot \frac{A\cdot L}{L},A=$

cross Section $\rho =$ density

on $M=\rho \cdot A$ $V_A=\sqrt{\frac{T}{\rho \cdot \pi \cdot {\left(2{\gamma }_B\right)}^2}}$ $V_B=\sqrt{\frac{T}{\rho \cdot \pi \cdot r_B^2}}$ $V_A/v_B=\frac{1}{2}$

Ans A