Fundamental frequency of a guitar string?

In summary, the question asked for the new fundamental frequency of a 63.5-cm-long string on an ordinary guitar that is tuned to produce the note B3 with a frequency of 245 Hz. By using the equation f_n = n\frac{v}{2L}, it was determined that the speed of transverse waves on the string is 311 m/s. When the tension in the string is increased by 1.0%, the new fundamental frequency is calculated to be 246 Hz. This demonstrates an understanding of proportionalities.
  • #1
erik-the-red
89
1
Question:

One of the 63.5-cm-long strings of an ordinary guitar is tuned to produce the note [tex]{\rm B_3}[/tex] (frequency 245 Hz) when vibrating in its fundamental mode.

1.

If the tension in this string is increased by 1.0%, what will be the new fundamental frequency of the string?

The first part of the question asked for the speed of transverse waves on the string.

I used the equation [tex]f_n = n\frac{v}{2L}[/tex]. The fundamental frequency is given, so [tex]f_1 = 245 = \frac{v}{2*.635}[/tex], so [tex]v = 311[/tex] m/s.

This is correct.

In approaching the second part, I'm thinking [tex]T_2 = 1.01T_1[/tex]. Since [tex]v = \sqrt{\frac{T}{\mu}}[/tex], should I assume that the new speed will be [tex]311 * \sqrt{1.01}[/tex]?

Thus giving a new fundamental frequency of 246 Hz?
 
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  • #2
Not only is this correct, it shows good insight into proportionalities. Keep it up!
 
  • #3


Yes, your approach is correct. The new tension will result in a slightly higher speed of the transverse waves on the string, leading to a slightly higher fundamental frequency of 246 Hz. This increase in tension will also affect the higher harmonics of the string, resulting in a slightly different overall sound. It is important to note that even small changes in tension can have a significant impact on the fundamental frequency and overall sound of a guitar string.
 

Q: What is the fundamental frequency of a guitar string?

The fundamental frequency of a guitar string is the lowest frequency at which the string vibrates when plucked. It is determined by the length, mass, and tension of the string.

Q: How is the fundamental frequency of a guitar string calculated?

The fundamental frequency of a guitar string can be calculated using the following formula: f = 1/2L√(T/μ), where L is the length of the string, T is the tension, and μ is the linear density of the string.

Q: What factors affect the fundamental frequency of a guitar string?

The fundamental frequency of a guitar string is affected by the length, mass, and tension of the string. The type of material of the string and the thickness of the string also play a role in determining the fundamental frequency.

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

The fundamental frequency of a guitar string can be changed by altering the length, mass, or tension of the string. This can be done by adjusting the tuning pegs, changing the type of string, or using a capo to change the effective length of the string.

Q: Why is the fundamental frequency important in guitar playing?

The fundamental frequency is important in guitar playing because it determines the pitch of the string. By adjusting the fundamental frequency, different notes can be produced, allowing for the creation of melodies and chords. It also affects the tone and timbre of the guitar string.

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