Calculating Tightrope Tension with Waves: Circus Performer Homework Solution

[sun]

Homework Statement

A circus performer stretches a tightrope 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 0.880 s to reach the opposite tower, 20.0 m away. If a 1 meter length of the rope has a mass of 0.255 kg, find the tension in the tightrope.

Homework Equations

v-f(lambda)
v=sqrt.(tension/mu)
mu=mass per unit length
tension=mg
f=1/t

The Attempt at a Solution

I solved for wave speed using v=f(lambda)
f=1/T=1/.88s=1.136Hz
Delta(x)=lambda=20m, so 20m x 1.136=22.72m/s

Tension=v^2(mu) = (22.72)^2(.225/20) or (22.72)^2(.225/1) ??

I'm not sure what I'm doing wrong. Suggestions would be appreciated.

thanks

 

[Doc Al]

I solved for wave speed.
f=1/T=1/.88s=1.136Hz
Delta(x)=lambda=20m, so 20mX1.136=22.72m/s

I'm not following all that calculation. You are not given any data about f, T, or lambda.

The speed can be found simply by v = d/t = 20/.88 = 22.72m/s.

Tension=v^2(mu) = (22.72)^2(.225/20) or (22.72)^2(.225/1) ??

.225 kg is the mass of a 1 m section; so mu = mass/length = .225 kg/m.

 

[sun]

i don't know what I'm doing wrong when i use 22.72 to calculate the tension in the rope using: v=sqrt.(tension/mu)

maybe I'm calculating mu incorrectly? any ideas?

thank you very much

 

[Doc Al]

maybe I'm calculating mu incorrectly? any ideas?

You used two versions of mu. One is right; one is wrong.

 

[sun]

from what I've read i believe mu=.225 is the correct one. Because that is the mass for every 1 meter of string. Regardless of the mu I've been using i still get an incorrect answer.

this is why I'm still a bit confused.

thank you

 

[sun]

suggestions as to what i may be doing wrong would be greatly appreciated.

 

[sun]

i get 116.15N when i solve for tension, but this is wrong.

I could really use some help as soon as possible, please.

thank you

 

[Doc Al]

typo!

i get 116.15N when i solve for tension, but this is wrong.

Here's the likely problem: In your first post you state the mass as 0.255 kg, but in later posts you use 0.225 kg. Recalculate the answer using the correct value.

 

[sun]

Pure Genius! :P

At the rate i was going, i definitely would not have noticed that. :(

thank you