1. A.Diederich– International University Bremen – USC – MMM Spring 2005 1 instrument ! air ! listener source ! medium ! receptor 1.The source emits. 2.The medium transmits. 3.The receptor detects, registers, or, in general, is affected in some specific way.

2. A.Diederich– International University Bremen – USC – MMM Spring 2005 2 Sound waves –Goldstein, pp. 331 – 339 –CWE, pp. 182 – 187 –Levine, pp. 332 – 338 –Howard & Angus, Chapter 1 –Warren, pp. 1 – 5

3. A.Diederich– International University Bremen – USC – MMM Spring 2005 3 Sound of a physical stimulus: pressure changes in the air

4. A.Diederich– International University Bremen – USC – MMM Spring 2005 4 Sound waves –are longitudinal waves. –are alternations of rarefaction and compression of an elastic medium (such as water, air, or walls) in which they travel. –are created by rapid movement of a source in mechanical contact with this medium. –can be transmitted for great distances. –cannot pass through a vacuum. –The speed of sound varies according to the medium in which it travels.

5. A.Diederich– International University Bremen – USC – MMM Spring 2005 5

6. 6 –Wavelength ( ): distance from one peak of the wave to the next –Cycle: the completion of a full sequence of air rarefaction and compression –Frequency (f): number of cycles a sound wave completes in one second –Hertz (Hz): unit (cycles per second) used to measure frequency of sound waves – = v/f (v: velocity (m s -1 )) –Pressure amplitude: measure of the size of the variation in air pressure caused by a sound wave

7. A.Diederich– International University Bremen – USC – MMM Spring 2005 7 –Phase: the particular point in the compression- rarefaction cycle of sound wave at one instant of time –Phase (in phase; out of phase; how much they are out of phase is expressed in terms of phase angle  )

8. A.Diederich– International University Bremen – USC – MMM Spring 2005 8 Pressure amplitude –Amount by which the wave causes the pressure to differ from the normal atmospheric pressure (which is 10 5 N/m 2 ; newtons/meter 2 ) –Maximum pressure variation the ear can tolerate (10 00Hz tone) : 30 N/m 2 –Minimum pressure variation the ear can detect (10 00Hz tone) : 2 £ 10 -5 N/m 2

9. A.Diederich– International University Bremen – USC – MMM Spring 2005 9 Sound Pressure Level (SPL) The decibel SPL value for a sound with pressure L P = 20 log (P/P 0 ) P: sound pressure amplitude being measured P 0 : 2 £ 10 -5 N/m 2 (logarithmic scale relative to some reference)

10. A.Diederich– International University Bremen – USC – MMM Spring 2005 10 Relation between sound pressure and decibel 10 1020 10040 100060 10 00080 100 000100 1 000 000120 10 000 000140 dB SPL Pressure (p/p 0 )

11. A.Diederich– International University Bremen – USC – MMM Spring 2005 11 Sound pressure levels (intensity levels) of various sound sources

12. A.Diederich– International University Bremen – USC – MMM Spring 2005 12 Frequency

13. A.Diederich– International University Bremen – USC – MMM Spring 2005 13 Piano keyboard, showing the frequencies associated with each note and the ranges of various other instruments

14. A.Diederich– International University Bremen – USC – MMM Spring 2005 14 Complex sound waves produced by musical instruments

15. A.Diederich– International University Bremen – USC – MMM Spring 2005 15 Jean-Baptiste Joseph Baron de Fourier 1768 - 1830 –Fourier-analysis: decomposing complex pattern into sine waves –Fourier-synthesis: adding sine waves to create a complex pattern

16. A.Diederich– International University Bremen – USC – MMM Spring 2005 16

17. A.Diederich– International University Bremen – USC – MMM Spring 2005 17 Gradually adding higher frequency sine waves of lower amplitude Gradually adding higher frequency sine waves of the same amplitude

18. A.Diederich– International University Bremen – USC – MMM Spring 2005 18 Additive synthesis –Fundamental frequency (or first harmonic): starting frequency for a complex sound –Harmonics: pure tones, each of which has a frequency that is a multiple of the fundamental

19. A.Diederich– International University Bremen – USC – MMM Spring 2005 19 Frequency spectrum Fundamental or first harmonic Second harmonic Third harmonic frequency: line's position amplitude: line's height