Sound and Acoustics
Contents
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.
- Objects, like rooms, trumpets, and springs, do not typically vibrate with simple traveling waves, as described above.
- 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
- Explore the properties of sine waves by running and interacting with the iPython notebook
- PD
- Open pd and run your first patch
- Create a patch that multiplies two numbers and display the result in a Number Box
- Run this patch to build an oscillator
- Modify the patch so that you can choose between two frequencies of oscillation, say 400 Hz and 1000 Hz
- Modify the patch so that you can control the amplitude and frequency of the oscillation; compare your answer with patch
- LB
- Connect power + oscillator + speaker
- Vary the volume of the speaker module
- Change from square to saw-tooth wave shape
- How did you vary the amplitude? Can you vary the phase?
- Use your ears to tune your oscillator to 440Hz (A)
- Connect your circuit to the breadboard and use the oscilloscope to measure the frequency and amplitude of your signal
- Change from square to saw-tooth wave shape
Rhythm versus Pitch
- LB
- Connect power + oscillator + speaker
- Vary the frequency of the oscillator from rhythm to pitch
- PD
- Explain this patch
Summing Waves
- PD
- Create a patch with that adds (mixes) the output of two oscillators; compare your answer with this patch
- LB
- Connect power + splitter + (oscillator | oscillator) + mixer + speaker
- Perform the following experiments first with PD then with LB:
- Vary the gains in the mixer to tune one oscillator to 440Hz (A) and the other one to 659.25Hz (E)
- Set the mixer to add the two oscillators
- Use the oscilloscope to investigate the shape of the resulting wave
- Repeat with one oscillator tuned to 440Hz (A) and the other one to 554.37Hz (C#)
- Repeat with both oscillators tuned to 440Hz (A)
Harmonic series
- PD
- Explain this patch
- LB
- Connect power + split + 2 oscillators + mixer + speaker
- 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
- Envelope
- Basic instruments: strings, wind, percussion
- 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?