Why Does the Second Harmonic Frequency Double in a Fixed Rope?

  • Thread starter Thread starter test2morrow
  • Start date Start date
  • Tags Tags
    Frequency Harmonic
AI Thread Summary
The fundamental frequency of a rope fixed at both ends is 30Hz, and the second harmonic frequency is calculated to be 60Hz. In the fundamental mode, the rope has one loop, corresponding to a wavelength of λ/2. For the second harmonic, the rope has two loops, which means the wavelength is halved. This relationship between frequency and wavelength explains why the second harmonic frequency doubles. Understanding these principles is essential for solving similar problems in wave mechanics.
test2morrow
Messages
15
Reaction score
0

Homework Statement



If the fundamental frequency for a rope fixed at both ends is 30Hz, what is the frequency of the second harmonic?


Homework Equations



v=f*wavelength



The Attempt at a Solution



correct answer is 60Hz. Can somebody please explain? Thank you.
 
Physics news on Phys.org
In the fundamental mode of vibration, the rope contains one loop which is λ/2. In the second harmonic the number of loops are two. Then what is the new wavelength?
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Raman Spectroscopy: Understanding Stokes and Anti-Stokes Lines
Replies
7
Views
2K
Calculating frequency of the second harmonic
Replies
2
Views
2K
Which Frequency is NOT Possible for a Vibrating String?
Replies
5
Views
2K
Frequency and wavelength of a wave on a vertical rope
Replies
4
Views
4K
Simple Harmonic Motion/Fundamental Frequency
Replies
5
Views
2K
Violin frequencies and harmonics
Replies
2
Views
4K
What is the Frequency of This Simple Harmonic Motion?
Replies
3
Views
2K
Music Mystery: 2(Vsound) for the 2nd Harmonic?
Replies
2
Views
2K
Standing Waves On Strings: Harmonic and Frequency Problem
Replies
2
Views
4K
Find two lowest frequencies standing wave
Replies
5
Views
6K

Hot Threads

Recent Insights

Back
Top