Fun with Math & Music

Transcription

1 Fun with Math & Music Electric Guitars Mathematics Department Mercyhurst University April 2017

2 Our Journey of Sound 1 Guitar Basics 2 Strings Make Sound Waves Changing Waves 3 Pick-ups & Electromagnetic Induction Electromagnetism Pick-Ups 4 From Electricity to Sound Amplification Loudspeaker 5 Conclusion (Mercyhurst) Fun with Math & Music April / 14

3 Guitar Basics Guitar Basics tuning keys Math in the Making neck strings from nut to bridge details of bridge keep higher on neck in tune thickness of strings curvature of fretboard truss rod nut headstock fretboard fret truss rod neck magnetic pickups bridge body output jack Figure: some important features of an electric guitar (Mercyhurst) Fun with Math & Music April / 14

4 Strings Make Sound Waves Waves transerval longitudinal Figure: transversal and longitudinal waves (Mercyhurst) Fun with Math & Music April / 14

5 Strings Make Sound Waves Transversal Waves y A t Wave Formula ( ) 2π y = A sin w t w Figure: graph of wave formula (Mercyhurst) Fun with Math & Music April / 14

6 Strings Make Sound Changing Waves How to Manipulate Waves why would we want to do this? (Mercyhurst) Fun with Math & Music April / 14

7 Strings Make Sound Changing Waves How to Manipulate Waves why would we want to do this? well, changing properties of the wave changes pitch (Mercyhurst) Fun with Math & Music April / 14

8 Strings Make Sound Changing Waves How to Manipulate Waves why would we want to do this? well, changing properties of the wave changes pitch and that makes music! (Mercyhurst) Fun with Math & Music April / 14

9 Strings Make Sound Changing Waves How to Manipulate Waves Pitch is Frequency f = v λ why would we want to do this? well, changing properties of the wave changes pitch and that makes music! (Mercyhurst) Fun with Math & Music April / 14

10 Strings Make Sound Changing Waves How to Manipulate Waves Pitch is Frequency f = v λ why would we want to do this? well, changing properties of the wave changes pitch and that makes music! Change Velocity T v = µ (Mercyhurst) Fun with Math & Music April / 14

11 Strings Make Sound Changing Waves How to Manipulate Waves Pitch is Frequency f = v λ why would we want to do this? well, changing properties of the wave changes pitch and that makes music! Change Velocity T v = µ Change Wavelength λ = v f (Mercyhurst) Fun with Math & Music April / 14

12 Strings Make Sound Changing Waves Simple Example note wavelength(m) frequency(hz) C D E F G A B Table: wavelengths and frequencies of notes when velocity is m/s. (Mercyhurst) Fun with Math & Music April / 14

13 Strings Make Sound Changing Waves Simple Example note wavelength(m) frequency(hz) C D E F G A B Table: wavelengths and frequencies of notes when velocity is m/s. (Mercyhurst) Fun with Math & Music April / 14

14 Strings Make Sound Changing Waves Simple Example note wavelength(m) frequency(hz) C D E F G A B Table: wavelengths and frequencies of notes when velocity is m/s. (Mercyhurst) Fun with Math & Music April / 14

15 Strings Make Sound Changing Waves Simple Example note wavelength(m) frequency(hz) C D E F G A B Table: wavelengths and frequencies of notes when velocity is m/s. (Mercyhurst) Fun with Math & Music April / 14

16 Pick-ups & Electromagnetic Induction Electromagnetism Magnets & Electromagnetism N Magnetic Flux Φ B = (t) B(r, t) da Electromotive Force S Figure: The magnetic field around a magnet E = N dφ B dt Maxwell-Faraday E = B t (Mercyhurst) Fun with Math & Music April / 14

17 Pick-ups & Electromagnetic Induction Pick-Ups Magnetic Pickups Cylindrical Magnets Top Plate Coil of Wire Bottom Plate Figure: The side view of a magnetic pickup (Mercyhurst) Fun with Math & Music April / 14

18 Pick-ups & Electromagnetic Induction Pick-Ups Fun Sidenote y self-perpetuating do not need a medium example: light z x B E Figure: An electromagnetic wave (Mercyhurst) Fun with Math & Music April / 14

19 From Electricity to Sound Amplification Amplification preamplifier tone control phase inverter power amplifier Figure: Typical stages of a guitar amplifier (Mercyhurst) Fun with Math & Music April / 14

20 From Electricity to Sound Loudspeaker Loudspeaker metal basket outer radial magnet paper cone inner radial magnet dust cap air vent voice coils inner radial magnet outer radial magnet suspension mechanisms Figure: side view of a speaker (Mercyhurst) Fun with Math & Music April / 14

21 From Electricity to Sound Loudspeaker Loudspeaker metal basket outer radial magnet paper cone Voice Coil Holds soundwave information from pickup inner radial magnet dust cap air vent voice coils inner radial magnet outer radial magnet suspension mechanisms Figure: side view of a speaker (Mercyhurst) Fun with Math & Music April / 14

22 From Electricity to Sound Loudspeaker Loudspeaker Voice Coil metal basket outer radial magnet paper cone Holds soundwave information from pickup inner radial magnet air vent voice coils dust cap Inner Radial Magnet Electromagnetism causes this to vibrate inner radial magnet outer radial magnet suspension mechanisms Figure: side view of a speaker (Mercyhurst) Fun with Math & Music April / 14

23 From Electricity to Sound Loudspeaker Loudspeaker Voice Coil metal basket outer radial magnet paper cone Holds soundwave information from pickup inner radial magnet air vent voice coils dust cap Inner Radial Magnet Electromagnetism causes this to vibrate inner radial magnet outer radial magnet Paper Cone Connected to the magnet, so it will vibrate too suspension mechanisms Figure: side view of a speaker (Mercyhurst) Fun with Math & Music April / 14

24 From Electricity to Sound Loudspeaker Loudspeaker Voice Coil metal basket outer radial magnet paper cone Holds soundwave information from pickup inner radial magnet air vent voice coils dust cap Inner Radial Magnet Electromagnetism causes this to vibrate inner radial magnet outer radial magnet suspension mechanisms Figure: side view of a speaker Paper Cone Connected to the magnet, so it will vibrate too Soundwaves Paper cone pushes are molecules, causing sound! (Mercyhurst) Fun with Math & Music April / 14

25 Conclusion Summary Electric guitars are awesome! I obviously only understand a fraction of how they work. I highly recommend playing around with petal effects and amplification effects. (Mercyhurst) Fun with Math & Music April / 14

26 Conclusion More information The Science of Electric Guitars and Guitar Electronics Stop Faking It: Sound (Mercyhurst) Fun with Math & Music April / 14

27 Conclusion Thank you! (Mercyhurst) Fun with Math & Music April / 14