Solving Wave Propagation Dilemma: Length Increase of 10%

[dimpledur]

Homework Statement

A wave takes 4s to travel form one end of the string to the other. Then the length is increased by 10%. Now how long does a wave take to travel the length of the spring?

Homework Equations

v = sqrt ( FL/m)
F = -kx

The Attempt at a Solution

If the original stretch was x, then an increase of ten percent would be:
1.1x.

So, if F = -kx, and since k is constant, if x increases by a factor of 1.1, then as does F. SO the tensional force is 1.1F the original.

v = sqrt ( 1.1F*L/m)
(delta d) / (delta t) = sqrt ( 1.1F*L/m)
taking the inverse:
(delta t) / (delta d) = sqrt ( m/1.1F*L)

where (delta d = 1.1L) since it has increased by ten percent.

So,

delta t = 1.1L*sqrt ( m/1.1F*L)
so the original delta t must increase by a factor of 1.1/sqrt(1.1)

?

?

 

[Delphi51]

So, if F = -kx, and since k is constant, if x increases by a factor of 1.1, then as does F.

I don't understand this. The question doesn't say anything about the force or tension changing. Making the string longer might DEcrease the force but it sure wouldn't increase it.

 

[dimpledur]

It's actually a spring, but I was under the impression if you stretched a spring, you increased the tension..

 

[Delphi51]

Oh, sorry - I was thinking of putting a longer string on a guitar!

Using "v = sqrt ( FL/m)", it would appear that F increases by 1.1 and L increases by 1.1.
So the new v is 1.1 times the old v.

 

[dimpledur]

I was under the impression that L/m was a constant, regardless of whether it was stretched, since m/L is the linear mass density.

 

[Delphi51]

so L is the length? If so, L increases by a factor of 1.1, doesn't it?
The mass per unit length would decrease when the length increases.

 

[dimpledur]

I came here because apparently the velocity does not change.. I don't get how it doesn't change, though/

 

[Delphi51]

Oh, that's the answer I got! Using L increases by a factor of 1.1 and v increases by a factor of 1.1 in the formula t = d/v.

 

[dimpledur]

lol ill check it out thanks