A uniform rope of length 12 m and mass6 kg hangs vertically from a rigid support . A block of mass2 kg is attached to the free end of the rope . A transverse pulse of wavelengths 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?

A uniform rope of length 12 m and mass6 kg hangs vertically from a rig

1.	A uniform rope of length 12 m and mass6 kg hangs vertically from a rigid support . A block of mass2 kg is attached to the free end of the rope . A transverse pulse of wavelengths 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» SOLUTION :Tension at the LOWER end of the rope , `T_(1) = 2 G = 2 xx 9.8 = 19.6 N` Tension at the upper end of rope , Let `v_(1) and v_(2)` be the SPEEDS of pulse at the lower and upper end , respectively . So `v = SQRT (((T_(1))/(m))), v_(2) = sqrt(((T_(2))/(m)))` On dividing , we get `(v_(2))/( v_(1)) = sqrt(((T_(2))/( T_(1)))) = sqrt(((78.4)/(19.6))) = sqrt(4) = 2` As frequency is independent of medium , therefore if `lambda_(1) and lambda_(2)` are wavelengths at lower and upper ends respectively . Then `v_(1) = n lambda_(1) and v_(2) = n lambda_(2)` So, `(lambda_(2))/(lambda_(1)) = (v_(2))/( v_(1)) = 2` Therefore , the wavelength of pulse at upper end ` = 2 lambda`. `= 2 xx 0.06 = 0.12 m`