Question

A string is 3.00 m long with a mass of 5.00 g. The string is held taut with an applied tension of 500.00 N. (a) If a transverse pulse is sent down the string, how long does it take the pulse to travel the whole length? (b) Now suppose we keep the same tension on a thinner string, with the same mass (5 g) but twice the length (6 m). How long does the pulse take to travel the length for this case?

Answer 1

Velocity of a pulse on a stretched string is given by

where T is the tension on the string and μ is the mass per unit length.

(a) μ = = 1.66 x 10^-3 kgm^-1

T = 500.00 N

v = 548.82 ms^-1

Time taken, t = Distance / velocity = 3.00 / 548.82 = 0.0054 s

(b) Here, length is 6.00 m with same mass and tension.

μ = = 0.83 x 10^-3 kgm^-1

T = 500.00 N

v = 776.15 ms^-1

Time taken, t = Distance / velocity = 6.00 / 776.15 = 0.0077 s