Question 15: Waves

Question

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

Accepted Answer

The velocity of transverse waves is given by $$v = \sqrt {{T \over m}} $$ where, T = Tension and m = mass per unit length of the wire. If r is the radius of the wire and $$ho$$ its density then,
$$m = \pi {r^2}ho $$
$$	herefore$$ $$v = \sqrt {{T \over m}}  = \sqrt {{T \over {\pi {r^2}ho }}} $$
$$	herefore$$ $${v_A} = {{\sqrt {{T_A}} } \over {{r_A}\sqrt {\pi ho } }}$$ and
$${v_B} = {{\sqrt {{T_B}} } \over {{r_B}\sqrt {\pi ho } }}$$
Now, $${{{v_A}} \over {{v_B}}} = \sqrt {{{{T_A}} \over {{T_B}}}} .\,{{{r_B}} \over {{r_A}}}$$
$$\because$$ $${r_A} = 2{r_B}$$ and $${T_A} = {1 \over 2}{T_B}$$
Hence, $${{{v_A}} \over {{v_B}}} = {1 \over {2\sqrt 2 }}$$

Answer

1 : 2

Answer

1 : $$\sqrt2$$

Answer

1 : 2$$\sqrt2$$

Answer

3 : 2$$\sqrt2$$

Waves

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

Choose the correct answer: