A uniform rope of length 10 m and mass 3 kg hangs vertically from a rigid support. A block of mass 1 kg is attached to the free end of the rople. A transverse pulse of wavelength 0.05 m is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is

A uniform rope of length 10 m and mass 3 kg hangs vertically from a ri

1.	A uniform rope of length 10 m and mass 3 kg hangs vertically from a rigid support. A block of mass 1 kg is attached to the free end of the rople. A transverse pulse of wavelength 0.05 m is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is
Answer» 0.10 m 0.12 m 0.16 m 0.18 m Solution :Since the ROPE has a mass, the tension ALONG its length is VARIABLE. At the top end, its tension is `(3+1)g N` or `4g N`. At the bottom end, its tension is 1g N. Now, SPEED of the TRANSVERSE wave on the string, `c=sqrt((T)/(mu))` `upsilonlambda=sqrt((T)/(mu))""(because c=upsilonlambda)` As frequency `upsilon and mu`, the linear density are constant, so `sqrt(T)/(lambda)`is a constant.