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Hearing Science

Hearing Science. HSLS 253. Joe Hu Chapter 2 Sinusoids, The Basic Sound. Review for Chapter 1. HSLS 253. Why are hearing beneficial for surviving?. How do we separate “target” sounds from the other?. What are the three physical attributes of sound ?.

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Hearing Science

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  1. Hearing Science HSLS 253 Joe Hu Chapter 2 Sinusoids, The Basic Sound

  2. Review for Chapter 1 HSLS 253 • Why are hearing beneficial for surviving? • How do we separate “target” sounds from the other? • What are the three physical attributes of sound? • What are the two theories of hearing?

  3. Chapter 2 Sinusoids, The Basic Sound Topics to be covered • Sinusoids • Frequency • Starting phase • Amplitude • Vibrations

  4. What produces sound? • Vibrating object • Inertia • Elasticity

  5. Sinusoids • Sine wave, Simple Harmonic Motion • Describes a particular relationship between displacement and time • Chalkboard illustration

  6. Sinusoid Period: 1 second/cycle 1 Hz Frequency: 10 mm Amplitude: Starting phase: 0 degree Figure 2.2

  7. A pendulum in motion A swinging pendulum traces a sinusoidal function.

  8. Motion of pendulum and sinusoid

  9. Equation of a Sine wave D(t)=A•sin(2••f•t+) Frequency Starting phase Instantaneous amplitude Time Baseline-to-peak amplitude

  10. One cycle When the sine wave begins and ends at the same point of the displacement after having taken on all possible values of D(t)

  11. Frequency (f)D(t) = A•sin(2••f•t) • It is the number of cycles per second • Unit of measurement: Hertz (Hz) • Pitch is the subjectivecorrelate tofrequency.

  12. Finding the frequency???

  13. Period (Pr) • The amount of time a sinusoid takes to complete one cycle • Unit of measurement is second Pr = 0.1 s

  14. Relation between f and Pr frequency = 1/peiord Or Period = 1/frequency Remember to use period in seconds!

  15. Complex periodic vibration Repetition frequency Repetition rate Figure 2.4

  16. Starting phasey = A•sin(2••f•t + ) • The time in the displacement cycle at which the object begins to vibrate • Defined in terms of degrees of angle

  17. A sinusoid with marks every 90 degrees. Know these commonly-used starting phase: 0°, 90°, 180°, and 270°

  18. In Phase

  19. Out of Phase

  20. Phase Lead/Lag

  21. A sinusoid with a 180 degree starting phase. Figure 2.5

  22. A sinusoid with a 90 degree starting phase. Figure 2.6

  23. Two sinusoids of the same frequency but different starting phases (90 degrees difference). Figure 2.8

  24. Two sinusoids of the different frequencies but the same starting phases. Instantaneous phase difference differs at different points in time (D,E,F,G). Figure 2.9

  25. AmplitudeD(t) = A•sin(2••f•t + ) • How far an object moves • Loudness is the subjective correlate to amplitude (i.e., stimulus intensity). • The instantaneous amplitude D(t) varies with time.

  26. Baseline-to-peak amplitude (A) Peak-to-peak amplitude (2A)

  27. Root-mean-square Amplitude • Rationale: to have equal weight for each data point, i.e., every data point is equally important • Steps • Take a square of the instantaneous amplitude of each data point • Sum all the squared values • Divide the sum by the number of data points • Take a square root of the averaged value

  28. Root-mean-square Amplitude • Amplitude of a sine wave can be expressed in three different manners • Baseline-to-peak amplitude = A • Peak-to-peak amplitude = 2A • Root-mean-square (rms) amplitude = 0.707A

  29. Peak vs. rms amplitude Simple sinusoid – peak amplitude Complex waveform – rms amplitude Figure 2.4 Figure 2.2

  30. Vibrations Mass and spring model of a vibratory system. Mass (inertia) Inertia: The resistance of any physical object to a change in its state of motion or rest. Spring (elasticity) Elasticity: The physical property of a material that returns to its original shape after the stress that made it deform is removed. Resistance (e.g. friction) Figure 2.1

  31. Free Vibration • No force is applied to the system after it is set in motion • With no resistance (e.g. friction) and no more external forces applied, a free vibration will keep moving forever

  32. Damped Vibration • Caused by ________ to a motion • Could be due to _______ • Amplitude dies out over time Resistance Friction Figure 2.10

  33. Damped Vibration • Animation for free and damped vibration Animation courtesy of Dr. Dan Russell, Kettering University

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