A circus performer stretches a tigthrope between two towers. He strikes one end of the rope and sends a wave along it toward the other tower. He notes that it takes the wave 0.800 s to reach the opposite tower, 20.0 m away. If a 1.00 m length of the rope has a mass of 0.350 kg. Find the tension in the tigthrope

218.75N

To find the tension in the tightrope, we need to use the wave speed equation and tension equation.

First, let's find the wave speed. The wave speed (v) is given by the formula:

v = distance / time

Given that the wave takes 0.800 s to travel 20.0 m, we can substitute these values into the equation:

v = 20.0 m / 0.800 s
v = 25.0 m/s

Now, let's find the mass per unit length of the rope. The mass per unit length (mu) is obtained by dividing the mass of a 1.00 m length of the rope by that length. We are given that the mass of a 1.00 m length of the rope is 0.350 kg. Thus:

mu = mass / length
mu = 0.350 kg / 1.00 m
mu = 0.350 kg/m

Finally, we can calculate the tension in the tightrope using the formula:

T = mu * v^2

Substituting the values we found:

T = (0.350 kg/m) * (25.0 m/s)^2
T = 0.350 kg/m * 625 m^2/s^2
T = 218.75 N

Therefore, the tension in the tightrope is 218.75 N.