welcome to good vibrations: using phyphox and guitars to
TRANSCRIPT
Welcome to Good vibrations: using Phyphox and guitars to probe waves
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Mark [email protected] @DocWhalley
Evaluation forms
• We can only provide free CPD because of the funding we receive from the DFE. The evidence we provide to DFE of our reach to teachers comes solely through these evaluation forms. They should only take a couple of minutes to complete. Thank you.
• The link was included with the joining instructions and will be resent with the link to the PowerPoint afterwards.
• The link to the evaluation form is:
• This will also be shared in the Chatbox.
• It may help if you open the evaluation form now, before the session starts, and then complete it once the session finishes.
• Even if you are attending all the sessions, please complete the evaluation each time
• Please include the postcode of the school where you teach or are training.
• Look at some of the physics around the sound made by a guitar (actually 1 string!)
• Use Phyphox to obtain data
• Use Excel to model vibrations of a string
• Relevant physics for A-level and GCSE Required Practical
• It is interesting!
• Finding Physics in everyday life and interests / Science Capital dimension
• Physics/maths/music/history
What are we going to do and why?
• Guitar
• Phyphox on your phone (keep your old phones, I will use 3 for this!)
• Excel
• Tape measure (to measure the fretboard) / metre rule
What do you need to do this yourself?
Phyphox: Tone Generator and Audio Scope
Phyphox: Audio Scope, Audio Spectrum, Audio Autocorrelation
You may expect an open string to produce a single note.
However it is more complicated…
A note on any instrument is not a single tone, but a complex mix – this is what makes every guitar, and every instrument, different
Understanding open strings
Phyphox – Tone generator and Audio Scope, Audio Spectrum (Spectrum and History)
Phyphox – guitar and Audio Scope, guitar and Audio Spectrum (Spectrum and History)
The string vibrates in multiple modes simultaneously.
The modes are multiples of half-wavelengths.
So what is happening?
Use the Audio Spectrum (History) tool – notice the regular harmonics
(Fourier analysis!)
The amplitude of these harmonics determines the “heard” note
The instrument design and construction changes the sustain and tone
You can produce pure notes on a guitar by forcing a node at the points shown on the previous slide (frets 12, 7, 5)
Using Phyphox
Excel
Guitars have frets at predetermined positions to produce pleasing sounds (note that our scale is one of many)
Equally tempered scales: the ratio of frequencies along successive frets should be: 122 = 1.05946
Equally tempered scales –
(645 mm scales length)
Notes along a string and scales
D string Degree Fret
Note on heptatonic scale
length (mm) [measured]*
Fraction (relative to whole string)*
Open length / fretted length (freq. ratio)* ideal fraction
Equally tempered theoretical fret positions (mm)
D I 0 D 645 1 1 1 645
1 610 0.946 1.057 608.7989317
E II 2 E 575 0.891 1.121 9/8 574.6296732
F 3 543 0.842 1.188 542.3781878
III 4 F# 512 0.793 1.260 5/4 511.9368393
G IV 5 G 484 0.750 1.333 4/3 483.2040323
6 457 0.709 1.411 456.0838739
A V 7 A 432 0.670 1.493 3/2 430.485853
8 408 0.633 1.581 406.3245386
B VI 9 B 385 0.600 1.675 5/3 383.5192946
C 10 363 0.563 1.777 361.9940106
VII 11 C# 343 0.532 1.880 15/8 341.6768479
D Octave 12 D 323 0.500 2.000 2/1 322.5
Some details about a D-string
* These are based on measurements from my guitar – guitars are different sizes and so these values are unique to each guitar
The spreadsheet shows the fundamental produced at each fret, up to the 12th fret (octave)
Excel, again
GCSE Required Practical
Why not use a guitar?
On each string, the tension remains unchanged and the mass/unit length is unchanged and so the wave speed is the same regardless of where the string is fretted (a bit of A-level there)
Measure the fundamental frequency at each fret, using Audio Autocorrelation
The length of the fretted string l = ½ , and so = 2 l
GCSE Required Practical
Processing data
• You could take an average of the wave speeds (in this case 192.7 m/s)
• or you could plot 1/f against length of string
Getting a value
v = f
but = 2 l
therefore v = 2 l f
1/f = (2/v) l
c.f. y = mx
therefore gradient = 2/v
v = 2 / gradient
in the above example v = 2 / 0.0106 = 188.7
m/s
Reference
String Frequency Scientific pitch notation
1 (E) 329.63 Hz E4
2 (B) 246.94 Hz B3
3 (G) 196.00 Hz G3
4 (D) 146.83 Hz D3
5 (A) 110.00 Hz A2
6 (E) 82.41 Hz E2
Reference
Phyphox allows you to cast your display, and control the play/pause.
Reference: Casting your phone to your computer
Touch here
Tick this boxType this into your browser address bar
Evaluation forms
• We can only provide free CPD because of the funding we receive from the DFE. The evidence we provide to DFE of our reach to teachers comes solely through these evaluation forms. They should only take a couple of minutes to complete. Thank you.
• The link was included with the joining instructions and will be resent with the link to the PowerPoint afterwards.
• The link to the evaluation form is:
• This will also be shared in the Chatbox.
• It may help if you open the evaluation form now, before the session starts, and then complete it once the session finishes.
• Even if you are attending all the sessions, please complete the evaluation each time
• Please include the postcode of the school where you teach or are training.
