Fundamental frequency of a guitar string

In summary, the conversation discusses the problem of finding the frequency of a guitar string with specific measurements. There is confusion about the distance used in the equation and the possibility of a calculation error. After making an adjustment to the mass used in the formula, the estimated frequency is 465 Hz.
  • #1
raw_rock7
1
0
1. The problem is: A guitar string is 78 cm long and has a mass of 3.6 g. The distance from the bridge to the support post is L = 60 cm, and the string is under a tension of 505 N. What is the frequency of the fundamental?
I don't get why it gives me two distances. Which one is L?




2. The equations I've been using haven't been working, so this is pretty much my problem.



3. When I plugged values into the equation f= sqrt(T/(m/L)) * 1/(2L), I got the answer of 241.762 Hz
 
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  • #2
I don't know much about this, but I wonder if there is a little trick in the mass.
It looks like you are only using 60 cm of a 78 cm string with mass 3.6g. So the mass you want to use in the formula would be 60/78*3.6 g.

I get 465 Hz with that small adjustment, which makes me think you made an error in your calculator work - or I did!
 
  • #3
. However, when I checked online, the correct answer is actually 225 Hz.

I understand your confusion about the given distances and the discrepancy in your calculated frequency compared to the correct answer found online. To clarify, the distance from the bridge to the support post (60 cm) is the length of the vibrating portion of the string, denoted as L in the equation. The total length of the string (78 cm) is needed to calculate the mass per unit length (m/L) of the string.

It is important to note that the equation f= sqrt(T/(m/L)) * 1/(2L) assumes that the string is perfectly taut and has uniform density. Real guitar strings, however, may have slight variations in density and may not be perfectly taut, which can lead to discrepancies in the calculated frequency.

Furthermore, it is possible that the online source you consulted used a different equation or method to calculate the fundamental frequency, resulting in a different answer. It is always important to double check your calculations and consult multiple sources to ensure accuracy.

In conclusion, the fundamental frequency of a guitar string can be calculated using the given equation, but slight variations in the real string and different calculation methods may result in discrepancies. It is important to understand the assumptions and limitations of any equations used in scientific calculations.
 

What is the fundamental frequency of a guitar string?

The fundamental frequency of a guitar string is the lowest frequency that a string can produce when it vibrates. It is also known as the first harmonic or the natural frequency.

How is the fundamental frequency of a guitar string determined?

The fundamental frequency of a guitar string is determined by its length, tension, and mass per unit length. The longer the string, the lower the fundamental frequency. Similarly, the tighter the string is stretched, the higher the fundamental frequency. Lastly, a heavier string will have a lower fundamental frequency compared to a lighter string.

What factors can affect the fundamental frequency of a guitar string?

Apart from its length, tension, and mass per unit length, the fundamental frequency of a guitar string can also be affected by the material of the string, the temperature, and the humidity. Different materials have different densities and stiffness, which can impact the fundamental frequency. Temperature and humidity can also affect the tension and mass of the string, thus altering the fundamental frequency.

How can the fundamental frequency of a guitar string be changed?

The fundamental frequency of a guitar string can be changed by altering its length, tension, or mass per unit length. This can be achieved by changing the fret position, tuning the string to a different note, or using a different gauge of string. Additionally, factors such as temperature and humidity can also have an impact on the fundamental frequency.

Why is the fundamental frequency of a guitar string important?

The fundamental frequency of a guitar string is important because it determines the pitch of the note produced by the string. It is also the basis for all the other harmonics or overtones that can be produced by the string. Understanding the fundamental frequency can help musicians in tuning their instruments and creating different sounds and effects while playing.

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