Calculating Frequency Changes in a Guitar String

In summary, the frequency of a guitar string 60 cm in length, with a diameter of 1.4 mm and a tension of 289 N, is 147 Hz. When the tension is reduced to 196 N, the frequency becomes 112.7 Hz. For a string of the same material, 45 cm long and 1 mm in diameter under 168 N of tension, the frequency is 209.8 Hz. The frequency is directly proportional to the square root of the tension.
  • #1
Shaley
12
0
A guitar string 60 cm in length, with a diameter of 1.4 mm and a tension of 289 N, emits a note with a frequence of 147 Hz. Find the frequency in each of the followig situations:

a)the tension isreduced to 196N
b)a string of the same material, 45 cm long and 1mm in diameter under 168 N of tension, is plucked.

I have no idea for a, but I was hoping someone could check my work on b?
=Fi(square root of tension fraction)(length fraction)(diameter fraction)
=147Hz(square root of 169/289)(60/45)(1.4/1)
=209.8Hz

I am just getting confused as to if the 289 goes on top of the fraction, or the 169.

thanks for your help in advance!
 
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  • #2
It would help if you put units in the equations then you can easily check that you have them the correct way around.

frequency = sqrt ( Tension / mass per unit length )
s-1 = sqrt ( N / Kg m -1 )
s-1 = sqrt ( kg m s-2 / Kg m -1 ) = sqrt(s-2)
 
  • #3
thankyou. Can you please help me with part a as well?
 
  • #4
The frequency is proprtional to sqrt(tension)
 
  • #5
thanks again
 

FAQ: Calculating Frequency Changes in a Guitar String

1. What is tension in a guitar string?

Tension in a guitar string refers to the amount of force or pull that is applied to the string. It is responsible for creating the sound and pitch of the string when it is plucked or strummed.

2. How is tension measured in a guitar string?

Tension in a guitar string is measured in units of pounds (lbs) or newtons (N). This measurement is typically calculated by using a tension gauge or by applying a known weight to the string and measuring the amount of deflection.

3. What factors affect the tension of a guitar string?

The tension of a guitar string is affected by several factors, such as the string material, string gauge, and tuning. Thicker strings and higher tuning will result in a higher tension, while thinner strings and lower tuning will result in a lower tension.

4. Why is tension important in guitar playing?

Tension is important in guitar playing because it directly affects the sound and playability of the instrument. The right amount of tension allows for a clear and consistent tone, while too much or too little tension can result in a muffled or out-of-tune sound.

5. How can tension in guitar strings be adjusted?

Tension in guitar strings can be adjusted by changing the string gauge, tuning, or by using a capo. Adjusting the tension can help achieve the desired sound and playability for different styles of music and playing techniques.

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