A uniform rope of length 10 cm and mass 4 kg hangs vertically from a rigid support. A block of mass 2 kg is attached to the free end of the rope. A transverse pulse of wavelength 0.06 m is produced at the lower end of the rope, what is the wavelength of the pulse when it reaches the top of the rope?

Explanation

As shown below, let the tension at point 1 and 2 are `T_(1) and T_(2)` respectively, then
`T_(1)=2g,T_(2)=6g`
If `V_(1) and V_(2)` are the speeds of wave at ends 1 and 2 respectively, then
`(V_(1))/(V_(2))=(flamda_(1))/(flamda_(2))=sqrt((T_(1)//mu)/(T_(2)//mu))=sqrt((T_(1))/(T_(2)))=sqrt((2g)/(6g))=sqrt((1)/(3))=(1)/(sqrt(3))`
`lamda_(2)=sqrt(3)lamda_(1)`
`=sqrt(3)xx0.06=0.06sqrt(3)m`