Lesson Summary 

Analyze resonance as it pertains to wave phenomena. 


Resonance - The quality of a system to oscillate at a higher amplitude at specific frequencies over others.  Musical instruments make use of resonance and dominant resonant frequencies. An interesting example of destructive resonance is the case of the Broughton Suspension Bridge.  The English suspension bridge collapsed in the 1830's due to a platoon of soldiers marching in time activating a resonant frequency of the bridge. 

Beating frequencies - The interference between two frequencies that are slightly different. Beats are perceived as variations in volume whose rate is the difference between the two frequencies. frequency 1 - frequency 2 = the beating frequency. 

Standing waves - Also known as a stationary wave, is a wave that stays in a constant position.  This can happen when two waves of identical frequency meet with such a phase alignment that through superposition they reinforce each other.   Standing waves and resonance are two concepts used throughout acoustic instrument creation. 

Node - The position in a standing wave where the wave has a minimum amplitude. 

Anti - node - The position in a standing wave where the wave has a maximum amplitude. 


Observe beating frequencies in the Werkstatt.


1 x Arduino Microcontroller

Jumper Cables


By using the LFO and VCO we can hear beating frequencies produced by the Werkstatt.  Match the Werkstatt settings to Figure 1 to begin. 



 Figure 1. VCO and LFO beating frequency settings.


Listen to the output changes as your turn the LFO RATE knob.  Because of the wide range of frequencies accessible by both the LFO and VCO slight knob turns will alter the beating frequency greatly. 

See if you can find more beating frequencies at other pitches using the VCO. 

What happens when you change the VCO MOD DEST switch from FREQ to PWM? What effect does this have on the sound and why?


To see what these beating frequencies look like we will need to plug our Werkstatt's audio output into an audio input on whatever computer we are using.  On my laptop I am simply changing the headphone output settings to allow the port to act as an input.  





Once we are sending signal into our computer we need to check that it is the primary audio input source.  If the Werkstatt is plugged into the primary audio input source then we are ready to run our Audio_In.pde program. Audio_In.pde also allows the user to increase the visual amplitude of the incoming audio as well as pause the wave animation.  These can be controlled by pressing the arrow keys. 

↑  Amplitude Increase

↓  Amplitude Decrease

←  Pause Animation

→   Play Animation

For more information refer to the comments in Figure 2.


  Figure 2. Screen capture



The animation shown in Figure 3 displays two beating square waves.  Notice the periodic change in amplitude and duty cycle, this is the beat between the two frequencies.  Experiment with LFO RATE and FREQ to view other beating frequency visual patterns. 


 Figure 3. Beating frequency example.


Processing is an open source programming environment and community.




The Arduino is a micro controller and programming environment for interactive systems.