2. INDEX
Pg 3- AIM, APPARATUS, and
THEORY.
Pg 4- DIAGRAMS
Pg 5- PROCEDURE
Pg 6- OBSERVATION TABLE
Pg 7- GRAPH and OBSERVATIONS
Pg 8- RESULT and PRECAUTIONS
3. AIM
To determine the relationship between the tension and the frequency of a guitar string
APPARATUS
A guitar, a mobile app for measuring frequency
THEORY
Guitar tunings assign pitches to the open strings of guitars, including acoustic
guitars, electric guitars, and classical guitars. There are usually 6 strings in a guitar.
Starting from below (when we put the guitar on our lap with the neck towards our
left), the strings are named E, B, G, D, A, E respectively. Thus, the first and last
strings are named the same, even though their frequency is different. Each of them
is of different frequency. If we have the mass of the string, the frequency of that
particular string, and the length of that particular string, it is possible to calculate the
tension in the string using the formula:
Where,
f=fundamental frequency
L=string length between fixed points
T=string tension
Ρ=string mass per unit length
The SI unit of Tension being Newton(N).
If we want to express it in kilograms(kg) instead of Newton, we can simply divide the
resultant formula by 9.81, as there are 9.81 Newtons of force in a kilogram. Therefore, the
resultant formula is:
The length of the string that we are taking is 640mm, or 0.64m.
In an ideally tuned guitar, the tension for each of the strings should almost be the same.
4. DIAGRAMS
FIG 1: Diagram labelling standard parts of an acoustic guitar(left) and an electric guitar(right)
FIG 2: First 4 vibrations of a string fastened at both ends
5. PROCEDURE
1.Take out the guitar. Use the frequency measuring
app to measure the frequency of the guitar as you
pluck it.
2.Pluck it atleast 4 more times. Every time it is
plucked, put your finger on it to stop the
frequency from ringing for a longer time so you
can pluck it again for the next trial.
3.After 5 trials, take the mean frequency of all the
trials and put it in the frequency column under the
table to find the tension.
4.Move on to the next string. In this way, find out
the mean frequency of all the strings.
5.Remove the strings from the guitar. Using an
electronic weighing scale, weigh each string and
find out their weight in kg/m.
7. GRAPH BETWEEN TENSION AND FREQUENCY
OBSERVATIONS
From the above graph, we observe that the tension is reasonably similar for all the strings of
the guitar. This is necessary to avoid unequal stress being inflicted on the body of the
instrument. It’s also the reason why all the strings end up feeling pretty much the same to
play.
8. RESULT
For an ideal guitar, for any string, the tension of each string is almost the same, i.e., it is
constant.
PRECAUTIONS
1. Take into account any zero error of the weighing scale.
2. Take care when removing the strings, as they might snap suddenly and hurt you.
