A 100g wire is held under a tension of 250 N with one end at x = 0 and the other x = 10m. At time t = 0, pulse 1 is sent along the wire from the end at x = 10m. At time t = 30ms, pulse 2 is sent along the wire from the x = 0. At what position x do the pulses begin to meet?

Answer 1

The mass per unit length of wire is
s = 0.1 kg/10 m = 10^-2 kg/m
The wave speed is
v = sqrt(T/s) = sqrt[250/10^-2] = 158.1 m/s
With a 30 ms delay of the second pulse, the first pulse will already have traveled x1 = 4.743 m. It will travel half of the remaining distance,
x2 = (1/2)(5.257) = 2.629 m,
before they meeet.
The meet at location x1 + x2.