Wave on a string under tension

BOYLANATOR

1. The problem statement, all variables and given/known data
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.

2. Relevant equations
v=√(F/u) u=m/L


3. 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.
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution

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

A spelling mistake. Thanks.

angular frequency is radiens per second.
me neither.
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.