Derive v = 2 l_nf_n for the nth harmonic

In summary, the equation for the nth harmonic of a vibrating string is v = 2 l_nf_n, where v is the velocity, l_n is the length of the string, and f_n is the frequency of the nth harmonic. This equation is derived from the fundamental principle of standing waves, which states that the wavelength of a standing wave on a string must be equal to twice the length of the string. The letter "n" represents the harmonic number, indicating the number of nodes or antinodes present in the standing wave. The harmonic number is squared because it represents the number of nodes present in the standing wave. This equation is used in various fields to study the properties of vibrating strings and other systems that exhibit standing waves.
  • #1
Northbysouth
249
2

Homework Statement


Derive the expression v = lnfn where ln is the shortest distance between nodes for the nth harmonic.


Homework Equations


v = wave speed
ln = shortest distance between nodes for the nthharmonic
fn = frequency of the nth harmonic


The Attempt at a Solution



Is it asking me to take the derivative of the wave speed, which I believe would give me the acceleration of the wave?

So,

wave acceleration = 2*ln

Am I making any sense?
 
Physics news on Phys.org
  • #2
nth harmonics of fo is n times fo. Similarly ln is equal to (lambda)o/2n.
Now proceed.
 

FAQ: Derive v = 2 l_nf_n for the nth harmonic

What is the equation for the nth harmonic of a vibrating string?

The equation is v = 2 l_nf_n, where v is the velocity, l_n is the length of the string, and f_n is the frequency of the nth harmonic.

How is this equation derived?

This equation is derived from the fundamental principle of standing waves on a string, which states that the wavelength of a standing wave on a string must be equal to twice the length of the string.

What does the letter "n" represent in this equation?

The letter "n" represents the harmonic number, which indicates the number of nodes or antinodes present in the standing wave. For example, the first harmonic (n=1) has one node and two antinodes, while the second harmonic (n=2) has two nodes and three antinodes.

Why is the harmonic number squared in this equation?

The harmonic number is squared because it represents the number of nodes that are present in the standing wave. Since standing waves occur when there is a fixed number of nodes and antinodes, the harmonic number must be squared to properly account for the number of nodes.

How is this equation used in scientific research?

This equation is used to calculate the velocity of a standing wave on a string, which is important in understanding the behavior of vibrations and waves. It is also used in various fields such as acoustics, music, and engineering to study the properties of vibrating strings and other systems that exhibit standing waves.

Similar threads

Superposition of two one-dimensional harmonic waves
Replies
10
Views
1K
Standing Waves On Strings: Harmonic and Frequency Problem
Replies
2
Views
3K
How to derive a formula for simple harmonic motion?
Replies
1
Views
1K
Which harmonics would be observed on an electric guitar?
Replies
3
Views
1K
How harmonics are produced in a guitar string?
Replies
11
Views
3K
Find two lowest frequencies standing wave
Replies
5
Views
6K
Solving Wave Speed of a Violin String
Replies
6
Views
3K
Calculating Mass of a Vibrating String Using Known Quantities
Replies
10
Views
2K
Calculating Standing Wave Diagrams and Wave Speeds for Closed Cylinders
Replies
1
Views
3K
Harmonic Oscillator- Is this correct?
Replies
1
Views
975

Hot Threads

Recent Insights

Back
Top