Wave on a string under tension


by BOYLANATOR
Tags: string, tension, wave
BOYLANATOR
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#1
Mar9-12, 04:20 AM
P: 173
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
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Simon Bridge
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#2
Mar9-12, 04:48 AM
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Welcome to PF.
Reasoning seems fine to me - notice how the number end up all nice?
Did you do the next bit?
BOYLANATOR
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#3
Mar9-12, 05:00 AM
P: 173
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
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#4
Mar9-12, 05:01 AM
P: 173

Wave on a string under tension


(where w is angular frequency)
Simon Bridge
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#5
Mar9-12, 05:19 AM
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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.


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