A uniform thin rope of length 12 m and mass 6 kg hangs vertically from a rigid support and block of mass 2kg is attached to its free end. A transverse short wave-train of wavelength 6 cm is produced at the lower end of the rope. What is the wavelength of the wavetrain (in cm) when it reaches the top of the rope?

Explanation

As the rope has a mass and a mass is also suspended from the lower end, the tension in the rope will be different at different points. Now as `v = sqrt((T//m))`
or `v_T/v_B =sqrt(T_T/T_B) = sqrt(((6 =2)g)/(2g) ) = 2(or) [(f_r lambda_T)/(f_blambda_B)] =2`
`[as v = f lambda]`
Here ` f_T =f_B` as frequency is the characteristic of the source producing the waves.
So `lambda_T =2 lambda_B = 2 xx 0.06 = 0.12 m`