How does a guitar work?

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
0 2L
1st harmonic 1 L
2nd harmonic 2 2/3 L
3rd 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 1st, 2nd and 3rd 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.