Fundamental frequency of violin string

In summary, the conversation discusses finding the fundamental frequency of a vibrating string on a violin when it is pressed against the fingerboard at a certain point. The length of the string is shortened by 60 mm, but this does not affect the frequency. The equations f = nv/2L and wavelength = v/f are used to solve the problem. The original frequency given is needed to find the fundamental frequency of the shortened string.
  • #1
Nano
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Homework Statement



A vibrating string on a violin is 330 mm long and has a fundamental frequency of 659 Hz. What is its fundamental frequency when the string is pressed against the fingerboard at a point 60 mm from its end?

*The answer is 805 Hz

Homework Equations


f = [tex]\overline{}nv[/tex]/2L
wavelength = v/f

The Attempt at a Solution


I don't understand what to do with the 60mm. It splits the string into 2 unequal parts, which isn't a harmonic I recognize.
 
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  • #2
I don't understand what to do with the 60mm. It splits the string into 2 unequal parts, which isn't a harmonic I recognize.
That's just telling you how much shorter the string is now. You are ignoring the 60mm part that is pinched off, and considering the length that remains. This is the length you are trying to find the fundamental frequency for.
 
  • #3
hage567 said:
That's just telling you how much shorter the string is now. You are ignoring the 60mm part that is pinched off, and considering the length that remains. This is the length you are trying to find the fundamental frequency for.

Oh, so there's no node there? So (330-60) mm (=270) is the new length, L, of the string. What do you do with the original frequency they gave you?
By the way, this is a string with a fixed node on both ends, right?
 
  • #4
Oh, so there's no node there? So (330-60) mm (=270) is the new length, L, of the string.
By the way, this is a string with a fixed node on both ends, right?
Yes, that's correct.
What do you do with the original frequency they gave you?

You will need it to figure out the fundamental frequency of the 270mm length of the string. :smile:

You have the equations you need to solve this. You just need to find a way to relate the first string to the second string.
 
  • #5
hage567 said:
Yes, that's correct.
You just need to find a way to relate the first string to the second string.

That's what I don't understand--how are the two connected? They're not harmonics. I keep trying to use the formula f = nv/2L, but that doesn't work and it doesn't use the original frequency.
Intuitively, it seems that shortening the length of an already-vibrating string would increase the frequency, but I don't know how to derive this mathematically.
 
  • #6
Oh ok, I got it--I assumed that the velocity was 343 m/s, but you have to use the original frequency to calculate it.
 

1. What is the fundamental frequency of a violin string?

The fundamental frequency of a violin string is the lowest frequency at which the string can vibrate and produce a sound. It is also known as the first harmonic or the first overtone.

2. How is the fundamental frequency of a violin string determined?

The fundamental frequency of a violin string is determined by its length, tension, and mass per unit length. These factors affect the speed at which the string vibrates and therefore, the frequency of the sound produced.

3. What is the relationship between the fundamental frequency and the pitch of a violin string?

The fundamental frequency of a violin string is directly proportional to the pitch of the sound produced. This means that as the fundamental frequency increases, the pitch of the sound also increases.

4. Can the fundamental frequency of a violin string be changed?

Yes, the fundamental frequency of a violin string can be changed by altering its length, tension, or mass per unit length. This can be done by adjusting the tuning pegs, applying pressure with the fingers, or using a different gauge of string.

5. Does the fundamental frequency of a violin string affect the sound quality?

Yes, the fundamental frequency of a violin string plays a significant role in determining the overall sound quality of the instrument. A string with a higher fundamental frequency will produce a higher pitched, brighter sound, while a string with a lower fundamental frequency will produce a lower pitched, warmer sound.

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