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

Explanation

The velocity of wave in string is given by `v=sqrt((T)/(mu))` where T is the tension and `mu` is the mass per unit length.since the tension in the string will increase as we move up the string ( as the string has mass) therefore the velocity will also
`therefore (v_("top"))/(v_("bottom"))=sqrt(T_("top")/(T_("bottom")))=sqrt(((6+2)g)/(2g))=2 therefore v_("top")=2v_("bottom")`
since frequency remains the same `therefore lambda_("top")=2lambda_("bottom")=2xx0.06=0.12m`