Sound and Acoustics

Waves

• What is a wave?
  • Translation of energy without translation of matter.
  • Waves travel through many types of media, even a vaccum!
  • Sound waves or acoustic waves are waves of mechanical & potential energy through a material.
• Acoustic waves exhibit polarization
  • The orientation of local movements versus propagation of the overal energy
  • Transverse
    • The local movements are perpendicular to the propagation (AKA shear waves)
  • Longitudinal
    • The local movements are parallel to the propagation (AKA compression waves)

Question: Are sound waves in air transverse or longitudinal?

• Reflections
  • When a wave hits a boundary, it reflects.
  • The reflection could either be the same as the incoming wave, or it could be inverted, depending on the change in impedance represented by the boundary.
    • Impedance is the resistance to change within the medium.
  • If the boundary is a change from low impedance to high impedance (like hitting a wall), the reflection is positive (not inverted).
  • If the boundary is a change from high impedance to low impedance (like the open end of a pipe), the reflection is negative.

• Standing Waves
  • Objects, like rooms, trumpets, and springs, do not typically vibrate with simple traveling waves, as described above.
    • Usually objects are finite
  • Standing Waves occur in finite objects
    • comprised of two waves- one traveling forward and one traveling backward.
    • depending on the boundary conditions, this changes the overall behavior of the vibrating object.
  • Check out this cool video.

• Demo: waves on 50' springs
  • Translation of energy w/o translation of matter - does the spring itself go somewhere?
  • Constant velocity - does a pulse travel the same speed across the whole spring?
  • Polarization - how do these look / do these move at the same speed across the spring?
  • Boundary conditions - does a wave along a spring with a fixed end reflect the same way as one with a free end?

Frequency, Amplitude and Phase

• A very simple type of wave motion is called sinusoidal.
  • This motion comes from the geometry of a circle.

• Every sinusoidal wave or sine wave can be characterized by three parameters:
  • Frequency
  • Phase
  • Amplitude

• iPython Notebook

1. Explore the properties of sine waves by running and interacting with the iPython notebook

• PD

1. Open pd and run your first patch
2. Create a patch that multiplies two numbers and display the result in a Number Box
3. Run this patch to build an oscillator
4. Modify the patch so that you can choose between two frequencies of oscillation, say 400 Hz and 1000 Hz
5. Modify the patch so that you can control the amplitude and frequency of the oscillation; compare your answer with patch

• LB

1. Connect power + oscillator + speaker
2. Vary the volume of the speaker module
3. Change from square to saw-tooth wave shape
4. How did you vary the amplitude? Can you vary the phase?
5. Use your ears to tune your oscillator to 440Hz (A)
6. Connect your circuit to the breadboard and use the oscilloscope to measure the frequency and amplitude of your signal
7. Change from square to saw-tooth wave shape

Rhythm versus Pitch

• LB

1. Connect power + oscillator + speaker
2. Vary the frequency of the oscillator from rhythm to pitch

• PD

1. Explain this patch

Summing Waves

• PD

1. Create a patch with that adds (mixes) the output of two oscillators; compare your answer with this patch

• LB

1. Connect power + splitter + (oscillator | oscillator) + mixer + speaker

• Perform the following experiments first with PD then with LB:

1. Vary the gains in the mixer to tune one oscillator to 440Hz (A) and the other one to 659.25Hz (E)
2. Set the mixer to add the two oscillators
3. Use the oscilloscope to investigate the shape of the resulting wave
4. Repeat with one oscillator tuned to 440Hz (A) and the other one to 554.37Hz (C#)
5. Repeat with both oscillators tuned to 440Hz (A)

Harmonic series

• PD

1. Explain this patch

• LB

1. Connect power + split + 2 oscillators + mixer + speaker
2. Vary the frequency of the two oscillators until:
   • they are in tune
   • you hear a beat
   • they are one octave apart
   • they are a third apart

Sound dynamics

1. Envelope
2. Basic instruments: strings, wind, percussion
3. Acoustics

Resources

Almost All About Waves, John R. Pierce, Dover Books on Physics, 2006.

cos(a+b): Can you derive the FM (Ring Modulation) from this?