Fundamental Frequency of 6m String Vibrating at 16.5Hz

In summary, the fundamental frequency of a string that is 6m long and vibrating with 3 loops is equal to the frequency of the source, which is 16.5Hz. The relevant equations for this type of question are fn = nf1, L1 = λ/4, v = fλ, and v = d/t. There are no figures or sketches provided, but a Google Images search for "string harmonics" can be helpful. The third harmonic diagram is accurate to the equation and the relationship between the third diagram and the fundamental frequency is unclear.
  • #1
ElegantSir
37
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A string that is 6m long is vibrating with 3 loops in it. The frequency of the source is 16.5Hz.
What is the fundamental frequency of the string?

For the life of me I can't figure out how to solve this question. I found out that the wavelength is 4.8m but that's about it. If I use the equation fn = nf1 this is all I seem to be getting when I plug in the numbers. fn = 1 * 16.5Hz which is still equal to 16.5Hz...Id like to know what I am missing here.
 
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  • #2
ElegantSir said:
A string that is 6m long is vibrating with 3 loops in it. The frequency of the source is 16.5Hz.
What is the fundamental frequency of the string?

For the life of me I can't figure out how to solve this question. I found out that the wavelength is 4.8m but that's about it. If I use the equation fn = nf1 this is all I seem to be getting when I plug in the numbers. fn = 1 * 16.5Hz which is still equal to 16.5Hz...Id like to know what I am missing here.

Please stop deleting the Homework Help Template. It is important for you to start your schoolwork threads using that template. For example, what are the "Relevant Equations" for this type of question?

Also, when there are "3 loops", what does that look like? Can you post a figure or a sketch? And when the string is vibrating at its fundamental frequency, what does that look like?
 
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  • #3
I apologize for that.

The equations that I have been given to use for this unit are:
fn = nf1 - n being the nunber of cycles and f1 being the frequency
L1 = λ / 4 - L1 being the resonant wavelength
v = fλ
v = d / t

There are no figures or sketches for the question, I am strictly just going off of the numbers that it has given me.
All I know about the fundamental frequency in regards to the question is that it is the lowest possible frequency that I am trying to find, using the equation fn = nf1 to find it.
 
  • #4
ElegantSir said:
I apologize for that.

The equations that I have been given to use for this unit are:
fn = nf1 - n being the nunber of cycles and f1 being the frequency
L1 = λ / 4 - L1 being the resonant wavelength
v = fλ
v = d / t

There are no figures or sketches for the question, I am strictly just going off of the numbers that it has given me.
All I know about the fundamental frequency in regards to the question is that it is the lowest possible frequency that I am trying to find, using the equation fn = nf1 to find it.

Well, it's pretty easy to use Google Images to find figures that can help you figure this out. I did a Google Images search on string harmonics, and got lots of figures like this one:

https://soundphysics.ius.edu/wp-content/uploads/2014/01/harmonics.jpg
harmonics.jpg


So when you say "3 loops", is that like the 3rd harmonic diagram? And what is the relationship between the 3rd harmonic and the fundamental frequency?
 
  • #5
The third harmonic diagram would be accurate to the equation. I am not sure what the relationships is between the third diagram and the fundamental frequency.
 
  • #6
ElegantSir said:
The third harmonic diagram would be accurate to the equation. I am not sure what the relationships is between the third diagram and the fundamental frequency.

Count the little loop thingies... :wink:
 

FAQ: Fundamental Frequency of 6m String Vibrating at 16.5Hz

What is the fundamental frequency of a 6m string vibrating at 16.5Hz?

The fundamental frequency of a string refers to the lowest frequency at which the string vibrates. In this case, the fundamental frequency of a 6m string vibrating at 16.5Hz would be 16.5Hz.

How is the fundamental frequency of a string determined?

The fundamental frequency of a string is determined by its length, tension, and mass per unit length. In the case of a 6m string vibrating at 16.5Hz, the length of the string and the tension applied to it would be the determining factors.

Why is the fundamental frequency important in string vibrations?

The fundamental frequency is important in string vibrations because it determines the pitch of the sound produced by the string. The lower the fundamental frequency, the lower the pitch of the sound and vice versa.

Can the fundamental frequency of a string be changed?

Yes, the fundamental frequency of a string can be changed by altering its length, tension, or mass per unit length. For example, tightening the string would increase the tension and therefore increase the fundamental frequency.

How does the fundamental frequency of a string affect the sound it produces?

The fundamental frequency of a string directly affects the pitch of the sound it produces. A higher fundamental frequency will produce a higher-pitched sound, while a lower fundamental frequency will produce a lower-pitched sound.

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