Working of a Guitar : A Classroom Activity To Investigate The Properties Of Waves

Show a guitar to your class. The first step to understanding it's working is a brief description of its construction. Only the parts that are relevant to our study need to be labelled. Click here for a labelled picture of an acoustic guitar for your reference. A guitar consists of the body, the neck and the headstock.

1. The headstock has the tuning pegs. One end of each string is tied here and the tension in the strings can be increased or decreased by turning these pegs. These are used for tuning.
   
2. The neck consists primarily of the fretboard which consists of frets. Fingers are placed at appropriate locations on the fretboard to press a string to a particular fret in order to produce different frequencies of sounds.
   
3. The body consists of the saddle, bridge and the soundhole. The other end of each of the strings is fixed to the bridge. The soundhole and sound box acts as an amplifier for the sound produced by the string.

Equipped with the basic knowledge of a guitar, students will now be able to connect their lessons to the instrument.Place this question to the class:

A vibrating string produces such little sound. How is a guitar even heard? How is the sound amplified?

A guitar is heard because the string forces the sound-box to vibrate along with it at the same frequency as the string which inturn forces the air particles inside it to vibrate at the same frequency. This whole system forces the surrounding air to vibrate along with it and this is how the sound is amplified. The tendency of a vibrating object to force another adjoining or interconnected object to vibrate is referred to as a forced vibration.

Now introduce students to the formula for the velocity of a wave. As stated earlier, the velocity of a wave is dependent only on the medium. Specifically, it is dependent on the 'mass per unit length' of the string and the 'tension' in the string. The formula is written as :

v = (T/µ)1/2 where,

v = velocity of wave; T = Tension in the wave; µ = mass per unit length of the string

In case of our guitar, tension in the string is varied by turning the tuning screws. The mass per unit length of each of the strings is different, the lowest string being of the lowest mass per unit length and the highest being of the greatest mass per unit length.

When a guitar string is plucked, standing waves are produced in it. Where are the nodes? Node on the left is the point at which you press on the fretboard or the beginning of the fretboard for the open string. The other node is where the string is tied at the bridge.

The length between these shows no nodes. What will be the realation between the length(L) of the string between these nodes and the wavelength(λ)?

L = 1/2 λ

Now write down the wave formula

v = f x λ

and ask your students to derive a relation between frequency produced, velocity of wave and length of guitar between the two nodes.

This relation comes out to be :

f = v / 2L where,

f = frequency of wave produced; v = velocity of wave in the medium; L = length of the string between the two nodes

Now we know all the parameters which control the frequency of the sound produced. These are :

1. The length can be varied by moving the finger on the fretboard.
   
2. The velocity is dependent on tension in the string. Tension is varied by turning the tuning screws.
   
3. The velocity is also dependent upon the mass per unit length. Different strings have different mass per unit length.

For each of these, ask your students how can the frequency be increased by varying each of these parameters.