Course:PHYS341/2018/Calendar/Lecture09
Phys341 Lecture 09: Summary and web references
2018.01.22
Textbook: Ch.8 (minus the parts dealing with relative phase)
Slide List
- Frequency analysis
- Quick review:
- A perceived sound wave consists of successive crests and troughs of pressure arriving at our ears.
- But, we do not perceive the wave motion.
- As we will see later, the ear naturally analyzes the sound in terms of frequency components.
- In computational terms, this is an example of Fourier Analysis: expressing a complicated wave form in terms of a sum of simpler “pure tones”, each of a distinct frequency.
- There are ways of doing this with a computer (to do it by hand would take forever)
- The human ear does it quite naturally (and very quickly)
- Pure (simple) tones
- A pure tone can be produced by simple harmonic vibration; it has a single, definite frequency. The waveform is a simple sine wave.
- Real sounds are generally a mixture of many different frequencies; the frequency components are called partials. The waveforms are more complicated.
- Musical sounds generally have partials whose frequencies are integer multiples of a lowest fundamental frequency (or very close to integer multiples); these partials are called harmonics.
- Any uniform one-dimensional thing (thin strings, air columns) tend to generate a harmonic series.
- Small deviations from the integer series is call inharmonicity (e.g. thick strings, air columns with varying cross section).
- Pure tone – in time and frequency
- Add two simple tones
- Add three simple tones
- Add three simple tones
- Musical tones
- Many more partials
- Strength of partials tends to decrease with frequency
- Original waveform generally not a sinusoid
- Triangle (string plucked in centre)
- Sawtooth (bowed string)
- Square wave (woodwind)
- Periodic pulses (human voice)
- Triangle wave
- Sawtooth
- Square wave
- Pulse train
- Formants
- Real musical instruments (incl. human voice) have complex, harmonic spectra
- Some regions of frequency space enhanced: “formants”
- We control the frequencies of our voice formants to distinguish vowels
- Trained singers have a formant ~ 3 kHz, which allows a solo voice to rise above, say, an orchestra
- Violin formant ~ 3 kHz controlled by the torsional oscillation of the bridge, which partly mimics the human voice
- Of which, more later
- Vibrato
- See https://en.wikipedia.org/wiki/Vibrato Introduction and section 1.
- Real sounds
- Pure tone: whistling
- Complex tone with non-harmonic partials: uniform bar
- Complex tone with harmonics: marimba bar, taut thin string
- Complex almost harmonic partials: piano string