Welcome to Good vibrations: using Phyphox and guitars to probe waves

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Mark Whalleymark.whalley@iop.org @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.

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• Even if you are attending all the sessions, please complete the evaluation each time

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• 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.

Thank you

Dr Mark Whalley

Education Manager

mark.whalley@iop.org @DocWhalley