Question

A uniform rope of length `12m` and mass `6kg` hangs vertically from a rigid support. A block of mass `2kg` is attached to the free end of the rope. A transverse pulse of wavelength `0.06m` is produced at the lower end of the rope. What is the wavelength of the pulse whwn it reaches the top of the rope?

Answer 1

KEY CONCEPT : The velocity of wave on the string is given by the formula
`v = sqrt((T)/(m))`
where `T` is the tension and `m` 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 of wave will also increse. (`m` is the same as the rope is uniform)
:. `(v_(1))/(v_(2)) = sqrt((T_(1))/(T_(2))) = sqrt((2 xx 9.8)/(8 xx 9.8)) = (1)/(2)` :. `v_(2) = 2v_(1)`
Since frequency remains the same
:. `lambda_(2) = 2lambda_(1) = 2 xx 0.06 = 0.12m`