# Homework Help: Tranverse waves

1. Feb 4, 2009

### dimpledur

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

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?

2. Relevant equations

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

3. 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)

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2. Feb 4, 2009

### Delphi51

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.

3. Feb 4, 2009

### dimpledur

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

4. Feb 4, 2009

### 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.

5. Feb 4, 2009

### 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.

6. Feb 4, 2009

### 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.

7. Feb 4, 2009

### dimpledur

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

8. Feb 4, 2009

### 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.

9. Feb 4, 2009

### dimpledur

lol ill check it out thanks