Odd (pretty) waveform for third harmonic of violin E-string

[Ethan B.]

I lightly placed my finger a quarter of the length down the E-string of a violin and drew the bow, forcing the third harmonic. I used an oscilloscope app to look at the waveform. I got this unusually regular pure pattern:

https://drive.google.com/file/d/0B9KQ4zoXAY2AQkU1dVowWjRCUTA/view?usp=sharing

It looks almost like two waves a semitone apart are superimposed, but I can only hear one note. The same pattern occurs when the finger is placed on any of the nodes of the third harmonic, and a similar pattern occurs on the A-string, but with a lower frequency.

How is this happening?

 

[DEvens]

http://en.wikipedia.org/wiki/Beat_(acoustics)

 

[Ethan B.]

http://en.wikipedia.org/wiki/Beat_(acoustics)

I know there's a beat note here, but how come I don't hear a separate tone or any beats? And where could this inaudible second tone be coming from? I'm also puzzled as to why there only seem to be 2 tones at play here, instead of the usual mess.

 

[Svein]

I count 12 or 13 high-frequency waves to one low-frequency beat. If it is 12, the low frequency is A, 3 octaves below the A string. If it is 13, the low frequency is G#, which is a third above an E 4 octaves down.

 

[tech99]

I lightly placed my finger a quarter of the length down the E-string of a violin and drew the bow, forcing the third harmonic. I used an oscilloscope app to look at the waveform. I got this unusually regular pure pattern:

https://drive.google.com/file/d/0B9KQ4zoXAY2AQkU1dVowWjRCUTA/view?usp=sharing

It looks almost like two waves a semitone apart are superimposed, but I can only hear one note. The same pattern occurs when the finger is placed on any of the nodes of the third harmonic, and a similar pattern occurs on the A-string, but with a lower frequency.

How is this happening?

I am wondering if you are seeing the sampling frequency of the digital CRO. I have found an analogue CRO is immune from these problems.

 

[stedwards]

You appear to be looking at two harmonics of the string with all other frequencies mostly suppressed. What frequencies you get also depends on how far up the string you place the bow (but you probably know this).

I calculate a frequency ratio of about 45:49, or about 9:10. This would correspond the 8th and 9th harmonics of the fundamental. Am I calculating wrong?

 

[Ethan B.]

You appear to be looking at two harmonics of the string with all other frequencies mostly suppressed. What frequencies you get also depends on how far up the string you place the bow (but you probably know this).

I calculate a frequency ratio of about 45:49, or about 9:10. This would correspond the 8th and 9th harmonics of the fundamental. Am I calculating wrong?

Hello,

As the finger stopped the quarter length of the string, there were 4 antinodes and therefore it was the third harmonic (you can actually see the antinodes if you do the same thing on the G-string). As for the calculations, I'm thinking there is the third harmonic and another tone very close to it that is interfering. I wonder if this might have something to do with the fact that both ends of the string do not rest on sharp corners but are instead held "roundly" around the bridge and the nut? Or, maybe it is a software inaccuracy, as tech99 speculates, although I somewhat doubt this as the pattern also shows up on the A-string. I got the same pattern wherever I placed the bow, even behind the finger.

Later, I found that these "wavy" (not jagged) patterns occur on notes that resonate very well, such as C# (the violin's overall resonant frequency) and F#.