Frequency Variations of Standing Waves in a Guitar String
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 :
- The length can be varied by moving the finger on the fretboard.
- The velocity is dependent on tension in the string. Tension is varied by turning the tuning screws.
- 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.