The guitar produces different pitches from each string because the strings have different masses and tensions. Heavier strings with more mass produce lower pitches, while lighter strings with less mass produce higher pitches. When plucked, each string vibrates at its fundamental frequency but also produces additional frequencies called overtones that combine to give each string its unique timbre. Tuning the guitar adjusts string tension and alters the resonant frequencies and pitches of the strings.

1. THE PHYSICS OF MUSIC
How does a guitar work?

2. THE BASIC WORKING
 All of the guitar strings are closed on both sides,
and so we can assume that all of them have the
same wavelength.
 𝑣 = 𝑓𝜆 where v is the velocity of the wave, f is
frequency and 𝜆 is wavelength.
 A guitar has 6 strings that are all roughly of the
same tension.
 However each of the strings have a different size,
therefore they have different mass per unit length μ.
 Since 𝑤𝑎𝑣𝑒 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 =
𝑇𝑒𝑛𝑠𝑖𝑜𝑛 𝑜𝑓 𝑠𝑡𝑟𝑖𝑛𝑔
𝜇
waves
pass through each of the strings with a different
velocity.

3.  Thus the frequency of the strings is also different. In
reality, this means that each string resonates at a
different frequency, thereby producing a different
sound.
 Hence the sound emitted by 1st string(least μ) is of
a higher pitch than the sound emitted by the 6th
string(highest μ) which has the lowest pitch.

4. OVERTONES
 If strumming a string produced only 1 note of a
single pitch, we wouldn’t have rock ’n’ roll. How
does this work?
 The variation in sound emitted comes from the
different overtones. The fundamental frequency
(lowest frequency at which the wave resonates) is
the single tone. (Diagram A on next slide)

6. THE HARMONICS AND ASSOCIATED
WAVELENGTHS
Number of
nodes
Wavelength
Fundamental
frequency/ 1st
harmonic
0 2L
2nd harmonic 1 L
3rd harmonic 2 2/3 L
4th harmonic 3 1/2 L
When the wave has multiple nodes, then different
harmonics are produced as can be seen in Diagram
B, C and D, the 2nd , 3rd and 4th harmonic
respectively.
A combination of these overtones produces the
music we hear.

7. WHAT DOES TUNING DO?
 Tuning a guitar by twisting the knobs either tightens
or loosens the strings slightly.
 By changing the tension in the sting, the velocity of
the wave can be changed.
 This means that the string now resonates at a
different frequency, giving it a different pitch and
sound.