How to see the overtones (harmonics) on a string

They come from the stationary waves produced by reflections from the end stationary points of a string.


The 2 dimensional analog could be a filled bathtub with water. Dropping something in causes a wave to expand until it is reflected back by the bathtub structure and so on.


The standing waves or harmonics of a string can be seen by stretching a rubber rope of 3 meters for example. Those used for sewing on cloths.


Two people hold each end.


One of them vibrates his-her hand until a frequency is found that reveals the first pattern. Then if that is the fundamental (the lowest permissible frequency), by doubling the frequency of the oscilation of the hand the second overtone (harmonic but overtone is more correct) is seen. Then at triple frequency the third overtone can be seen.


The energy of the wave is reflected by the human hands holding the string. Those repeated reflections create a looping process, the oscilation itself. And the reaction pulses can be easily felt.


Tensioning the string or shortening it changes the reasonant frequencies as tensioning changes the speed of motion of the mechanical wave inside the string- rubber rope.


Same with musical instruments.


When we play C3 on a piano if we listen carefully we can hear many overtones.


One way to teach ourselves listening fir them is by holding C3 until the sound fully decays.


Then playing C4 for 2 seconds and releasing.


The string of the C3 which is still pressed will vibrate sympathetically to the fundamental of C4 so we can hear C4 being played from the string C3!


When we then play C3 normally your brain can more easily understand that those C3, C4 frequencies co exist. And they make the sound of a single note fuller.


In fact any note, A3 for example having a fundamental frequency of 220Hz contains many overtones called the harmonic series.


A bit higher than 2x220Hz which sounds A4.


A bit higher than 3x220Hz which sounds C4.


A bit higher than 4x 220Hz which sounds A5.


A bit higher than 5x220Hz which sounds C#5


and so on.


In the major scale is derived from the heamonic overtone series. This is why there is a DO RE MI FA SOL LA SI. And from just three notes most music is created.


References:


Musical Acoustics - Donald Hall


Waves - F.S. Crawford Jr - Berkeley Physics Course


Bernstein Harvard Lecture - YouTube