Question 446: Waves

Question

A uniform rope of length L and mass m
1
hangs vertically from a rigid support. A block of mass m
2
is attached to the free end of the rope. A transverse  pulse of wavelength $$\lambda $$
1
is produced at the lower end of the rope.  The wavelength of the pulse when  it reaches the top of the rope is $$\lambda $$
2
. The  ratio  $$\lambda $$
2
/$$\lambda $$
1
is

Accepted Answer

Wavelength of pulse at the lower end
$${\lambda _1} \propto velocity({v_1}) = \sqrt {{{{T_1}} \over \mu }} $$
Similarly, $${\lambda _1} \propto {v_2}$$ $$ = \sqrt {{{{T_2}} \over \mu }} $$
$$ 	herefore $$ $${{{\lambda _2}} \over {{\lambda _1}}} = \sqrt {{{{T_2}} \over {{T_1}}}}  = \sqrt {{{\left( {{m_1} + {m_2}} ight)g} \over {{m_2}g}}} $$
$$ = \sqrt {{{{m_1} + {m_2}} \over {{m_2}}}} $$

Answer

$$\sqrt {{{{m_2}} \over {{m_1}}}} $$

Answer

$$\sqrt {{{{m_1} + {m_2}} \over {{m_1}}}} $$

Answer

$$\sqrt {{{{m_1}} \over {{m_2}}}} $$

Answer

$$\sqrt {{{{m_1} + {m_2}} \over {{m_2}}}} $$

Waves

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