Transverse waves of same frequency are generated in two steel wir… - Vidyadip

MCQ

Transverse waves of same frequency are generated in two steel wires $A$ and $B$. The diameter of $A$ is twice of $B$ and the tension in $A$ is half that in $B$. The ratio of velocities of wave in $A$ and $B$ is

A
$1\;:\;3\sqrt 2 $
✓
$1\;:\;2\sqrt 2 $
C
$1\;:\;2$
D
$\sqrt 2 \;:\;1$

✓

Answer

Correct option: B.

$1\;:\;2\sqrt 2 $

b
(b) $v = \sqrt {\frac{T}{m}} = \sqrt {\frac{T}{{\pi {r^2}\rho }}} $

$v \propto \frac{{\sqrt T }}{r} $

$\Rightarrow \frac{{{v_A}}}{{{v_B}}} = \sqrt {\frac{{{T_A}}}{{{T_B}}}} .\frac{{{r_B}}}{{{r_A}}} = \sqrt {\frac{1}{2}} .\frac{1}{2} = \frac{1}{{2\sqrt 2 }}$

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