Question

A taut clothesline has length L and a mass M. Atransverse pulse is produced by plucking one end of theclothesline. If the pulse makes nround trips along theclothesline in t seconds.(a) Find the expression for the speed of thepulse in terms of n, L, and t.
1

(b) Find the expression for the tension F in theclothesline in terms of the same variables and mass M.
2

Answer 1

A taut clothesline has length L and a mass M. Atransverse pulse is produced by plucking one end of theclothesline. If the pulse makesn round trips along theclothesline in t seconds.(a) Find the expression for the speed of thepulse in terms of n, L, and t.

time period=n/t
frequency=1/T=t/n
so t/n=1/2L√T/m
now T=4L*L*m*t/n=4MLt/n

linear density=m=M/L
let the tension be T
speed=√T/m=√T*L/M=√4L*Lt/n=2L√t/n m/sec
1

(b) Find the expression for the tension F in theclothesline in terms of the same variables and mass M.
T=4L*L*m*t/n=4MLt/n N

2

Answer 2

a) Since the pulse makes n round trips, it travels 2L distance n times in time t.

∴the speed of the pulse is,

v = 2nL/t

b) Speed of the pulse is also given as,

v = √(FL/m)

∴ F = v2m/L

∴ F = (2nL/t)2(m/L) = (2n/t)2mL