Question

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 1

As the rope is heavy its tension will be different at different point. The tensinN/At the free end will be 92kg)g and that at the upper end it will be (8kg)g.

We have `v=vlamda`
`or sqrt(F/mu)=vlamda`
`or sqrtF/lmda=vsqrtmu`
The frequency of the wave pulse will be same everywhere on the rope as it depends only onthe frequency of the source The mass per unit length is also the same throughout the rope as ilt is uniform. thus, by
`i. sqrtF/lamda` is constant
Hence` sqrt(((2kg)g))/(0.06m)=sqrt(((8kg)g))/lamda_1`
`lamda_1` is the wavelength at the top of the rope. This gives `lamda_1=0.12m.