Question

A rope of mass 6 kg, hangs vertically from a rigid
support. A block of mass 2 kg is attached to the free
end of the rope. A transverse wave pulse of
wavelength 0.5 m is produced at lower end of the
ope. The wavelength of pulse, when it reaches the
top of the rope is
(1) 0.5 m
(2) 0.25 m
3) 0.75 m
4) 1.0 m​

Answer 1

Answer:

The answer is very shot,

0.5m

0.25m

0.75m

1.0m

2.50m

Answer 2

Answer is option 4 " 1.0 m"

Explanation:

• wavelength is directly proportional to square root of mass initially when wave enters from lower end it has tension which is sum of both the masses  and finally when wave reaches the top end the mass only produce tension is 2 kg

• So, $\frac{λ_{2} }{λ_{2} }$ = $\sqrt{\frac{m_{2} }{m_{1} } }$ = $\sqrt{\frac{6+2}{2} }$ = $\sqrt{\frac{8}{2} }$ = $\sqrt{4}$ = 2

• $λ_{2}$ = 2$λ_{1}$ ,$λ_{2}$ =  2 X 0.5 m
• $λ_{2}$ = 1.0 m
• hence, the right answer is option 4  "1.0 m"