What is the Length of a Tensioned String?

[BOYLANATOR]

Homework Statement

A pulse takes 0.1s to travel the length of a string. The tension in the string is provided by passing the string over a pulley to a weight which has 100 times the mass of the string.
What is the length (L) of the string?
What is the equation of the third normal mode.

Homework Equations

v=√(F/u) u=m/L

The Attempt at a Solution

We have L/t = √(100.m.g/(m/L) where g = surface gravity

So 100L^2 = 100gL
so L= magnitude(g) = 9.8 m

This type of question was not covered directly in our notes and I am unsure if my working is correct.
Thanks for any help.

 

[Simon Bridge]

Welcome to PF.
Reasoning seems fine to me - notice how the number end up all nice?
Did you do the next bit?

 

[BOYLANATOR]

It was the simplicity in the final answer that made me doubt it.
Thank you, but what is LQ?

y_3 = (A_3)sin(n.pi.x/L)cos((w_n)t)

We have 1.5 waves in a time of 0.1s. So w = 30.pi radians
I don't see how I can get the amplitude.

So y = A sin(3.pi.x/9.8)cos(30.pi.t)

 

[BOYLANATOR]

(where w is angular frequency)

 

[Simon Bridge]

but what is LQ?

A spelling mistake. Thanks.

angular frequency is radiens per second.

I don't see how I can get the amplitude.

me neither.

It was the simplicity in the final answer that made me doubt it.

I suppose with all the computer-randomized problems you get these days, nice numbers must be rare.

Note: cannot comment on answers as such - only methods and reasoning.