Velocity of Transverse Waves problem

rusty65

1. The problem statement, all variables and given/known data
Two children are sending signals along a cord of total mass 0.54 kg tied between tin cans with a tension of 37 N. It takes the vibrations in the string 0.53 s to go from one child to the other. How far apart are the children?

Express your answer using two significant figures


2. Relevant equations
Velocity of transverse wave on a cord = sqrt(F_t/[itex]\mu[/itex])
F_t = Tension Force
[itex]\mu[/itex] = mass per unit length -> m/l

3. The attempt at a solution
I attempted plugging the given values into the formula for velocity of a transverse wave on a cord, and came up with a distance of 4.387 meters. However, after getting the problem wrong (on masterphysics) I realized that the mass given for the cord is its total mass rather than mass per unit length. Seeing as what I am asked to find is the distance between the children (length of the cord) I dont see any way of solving this problem. Am i simply missing the proper formula? Any help would be greatly appreciated.

Infinitum

Hello rusty65!!

The mass per unit length, as you've written in your relevant equations is m/l. Putting this into the velocity equation and multiplying by time,

[itex]vt = t\sqrt{\frac{lF}{{m}}}[/itex]

What is "vt" in that above equation?

rusty65

vt is equal to the distance, but the trouble im having is that the distance, d, that i am attempting to find is equal to the length of the string, l. So i must either be using the wrong formula, or some key piece of information is escaping me.

This is where im at right now, using the information given:

d = t√((F_t * l)/m) ---plugged in----> d = 0.53√(37l/0.54)

So ive still got two unknowns, d and l, which, according to the wording of the problem, seem to me to be equal to one another.

rusty65

Scratch that, I figured it out!

Since d = l, I replaced l with d in the equation.

d = 0.53sqrt(37l/0.54) ---> d = 0.53sqrt(37d/0.54)
d/sqrt(d) = 0.53sqrt(37/0.54) ---> d/sqrt(d) = 4.387
d/sqrt(d) = d^(1/2) ---> sqrt(d) = 4.387
d = (4.387)^2
d = 19.246!

Took me a while to get it through my thick head, but I got it now. And thanks for the help!

Infinitum

Yep! That is what I was suggesting. Good to see you figured it out