A uniform rope of length 12 mm and 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 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?

Answer

`0.12 m`

Explanation

`V_("bottom")=sqrt((T)/(mu))=sqrt((2xx10)/(1//2))=2sqrt(10)m//s`
`V_("top")=sqrt((T)/(mu))=sqrt((8xx10)/(1//2))=4sqrt(10)m//s`
`rArr f=(V_("top"))/(lamda_("top"))=(V_("bottom"))/(lamda_("bottom"))rArr lamda_("top")=(4 sqrt(10))/(2 sqrt(10))xx0.06=0.12 m`