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

Harmonics on a Stretched Spring

  • Thread starter BuBbLeS01
  • Start date
602
0
1. Homework Statement
A. A string with a mass density μ = 4.10×10-3 kg/m is under a tension of F = 327 N and is fixed at both ends. One of its resonance frequencies is 742.0 Hz. The next higher resonance frequency is 1113.0 Hz. What is the fundamental frequency of this string?

B. Which harmonic does the resonance frequency at 742.0 Hz correspond to? (i.e. what is n at this frequency?)


C. What is the length of the string?


2. Homework Equations



3. The Attempt at a Solution
So for A. I wanted to use the equation...
FF = 1/2L * sqrt(T/μ)
FF - fundamental frequency
Where...
μ = 4.10×10-3 kg/m
T = 327N
but I don't know what L is?
 

andrevdh

Homework Helper
2,126
116
The standing waves in a string forms with integral multiples of half of the wavelength of the generated wave in the string

[tex]L = n\frac{\lambda}{2}[/tex]

and for the speed in the wave we can substitute

[tex]\lambda f = \alpha[/tex]

where

[tex]\alpha = \sqrt{\frac{T}{\mu}}[/tex]

giving

[tex] \lambda = \frac{1}{f} \alpha[/tex]

lets say that the one standing wave forms such that

[tex] L = \frac{n\lambda _1}{2}[/tex]

and the next harmonic such that

[tex] L = \frac{(n + 1) \lambda _2}{2}[/tex]

equating gives

[tex]\frac{n\lambda _1}{2} = \frac{(n + 1) \lambda _2}{2}[/tex]

therefore

[tex]n\lambda _1 = (n + 1) \lambda _2[/tex]

substituting now for [tex]\lambda[/tex] gives

[tex] \frac{n \alpha}{f_1} = \frac{(n+1) \alpha}{f_2} [/tex]

.......
 
Last edited:
602
0
Wow...okay so is that all just for the first part of the question??
 
602
0
Ok I got the answer for A and B (A was 371Hz and B was 2)....but I can not figure out how to determine the length of the string. I thought the equation to use was...
L = V/2f
but I don't have the velocity...
Can someone please help me with this.
Thank you
 

Related Threads for: Harmonics on a Stretched Spring

Replies
2
Views
2K
Replies
1
Views
3K
  • Posted
Replies
6
Views
9K
  • Posted
Replies
9
Views
4K
  • Posted
Replies
6
Views
1K
  • Posted
Replies
4
Views
4K
  • Posted
Replies
3
Views
2K
  • Posted
Replies
1
Views
693

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top