• Support PF! Buy your school textbooks, materials and every day products Here!

Fundamental Frequency Question

  • Thread starter dantechiesa
  • Start date
  • #1
dantechiesa

Homework Statement


A stretched wire vibrates in its first normal mode at a frequency of 369Hz. What would be the fundamental frequency if the wire were one third as long, its diameter were tripled, and its tension were increased two-fold?


Homework Equations



f = 1/2L * squareroot(Ft/u)

The Attempt at a Solution


[/B]
Can someone explain what I've done wrong?

369 = 1/2L * Sroot(Ft/u)

L is 1/3, so 1/2L becomes 3/(2L)

The Ft is doubled, but the u needs to be broken down further.
m/l = u
l is 1/3
m = dv
d stays the same, so v is the relevant one.
V = pi r2h
r is tripled, so the V increases by a factor of 9. However, since the h (aka l) also changes by a third. Total change of V is x3.

so, 3*m / (l/3)
All together,
Sroot ( 2Ft / (9u)

However, 369 * (3/2) * Sqroot (2/9) is wrong. ( = 260.922402258)

Thanks.
 

Answers and Replies

  • #2
mjc123
Science Advisor
Homework Helper
919
424
You had a factor of 1/2L. Now you have a factor of 3/2L. So you don't multiply by 3/2.
 
  • #3
Delta2
Homework Helper
Insights Author
Gold Member
2,423
683
Diameter is tripled

In the formula for V , r is the radius , so since diameter is tripled, radius goes up by x1.5.
 
  • #4
mjc123
Science Advisor
Homework Helper
919
424
Radius and diameter are in proportion. If one is tripled, so is the other.
 
  • #5
dantechiesa
You had a factor of 1/2L. Now you have a factor of 3/2L. So you don't multiply by 3/2.
Oh would you multiply by 3 only? Since the 1/2 was already apart of the equation?

ALso, does the remaining work with the square root seem right?

Thanks.
 
  • #6
mjc123
Science Advisor
Homework Helper
919
424
Yes
 
  • #7
dantechiesa

Related Threads for: Fundamental Frequency Question

  • Last Post
Replies
2
Views
6K
Replies
2
Views
5K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
5
Views
8K
Top