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Hearing Science

Hearing Science. HSLS 253. Chapter 3 Sound Transmission. Review for Chapter 2. HSLS 253. What is inertia and what is elasticity ?. What is the equation of a sine wave ?. What does each parameter represent?. What is “ in phase ” and what is “ out of phase ”?.

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Hearing Science

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  1. Hearing Science HSLS 253 Chapter 3 Sound Transmission

  2. Review for Chapter 2 HSLS 253 • What is inertia and what is elasticity? • What is the equation of a sine wave? • What does each parameter represent? • What is “in phase” and what is “out of phase”? • How do we measure rms amplitude? Why? • What is the relationship between rms and peak amplitude? • What are the two factors that give a vibration?

  3. Chapter 3 Sound Transmission Topics to be covered • Sound propagation • Pressure and intensity • Decibels • Interference • Sound fields

  4. Sound Propagation • When a body vibrates, areas of condensation are alternating over space with areas of rarefaction. animation of sound propagation (longitudinal wave) animation of sound propagation (spherical manner) Animation courtesy of Dr. Dan Russell, Kettering University

  5. Gas Laws When the object moves away from its resting state, it creates an area of greater density of air molecules. The density of air molecules increases, the pressure increases. This creates an area of _____________ condensation When the object moves back toward its resting state, air molecules will eventually fill the space they occupy. Now the density of air molecules has decreased, and thus, the pressure is lower. This creates an area of __________ rarefaction

  6. Sound Propagation • Static pressure • Condensation • Rarefaction Figure 3.1

  7. Wavelength () The distance between any successive identical points  = c • period  = c / frequency speed of sound in air: c = 345 (m/s) faster The speed of sound is _______ in a hot, humid area. increases Also, as the density of air molecules increases, the speed of sound __________.

  8. Pressure and Intensity • Chalkboard illustration…

  9. Pressure Pressure (p) is force per unit area p = F/Ar F = Force, Ar = Area Intensity (I) is proportional to pressure squared I = p2/ (0c) 0 - density of the medium; c – speed of sound

  10. Scale for sound intensity • Imagine: • If the softest perceptible sound was “1” • Then the loudest sound would be 100 trillion! • 100,000,000,000,000 or 1014 • This is way too big of a difference in practice • So we compress that range with logarithms • Remember this, we’ll come back to it

  11. Logs and Bels • A Bel is the log of a fraction • Log(X1/X2) = x Bels • X2 is the reference

  12. Bels and “deci” Bels (dB) • A deciBelis 10 times a Bel • If Log(X1/X2) = x Bels • Then 10 Log (X1/X2) = x deciBels or dB • Remember the equation 10 Log (X1/X2) is for intensity. However, in real life what we measure is sound pressure, so we will use the equation: • 20 Log (X1/X2)

  13. Bels and “deci” Bels (dB) • Example: • I am 6 feet tall. My daughter is 3 feet tall. How much taller am I than my daughter in dB? • Who is the reference? • My daughter • So dB = 20 Log (Hme/Hmy daughter)

  14. Back to our hearing example… • Logarithm of the fraction(in our example 1014 and 1) • Log(100,000,000,000,000/1) = 14 Bels • In dB: • 10 Log(100,000,000,000,000/1) = 140 deciBels, or dB • In general: • For intensity: dB = 10 log (I1/I2) • For pressure: dB = 20 log (P1/P2) • Intensity is proportional to pressure squared

  15. deciBels • 10 Log(1014/1) = 140 deciBels, or dB • In words: • The loudest sound we can tolerate (before bad things happen) is 140 deciBels above the softest sound we can detect • In this way, it is a relative measure • For the softest sound (the reference): • Intensity: 10-12 W/m2 • Pressure: 20 microPascals

  16. Example: 60 dB above the softest detectable sound for pressure • We know: • For pressure: dB = 20 log (P1/P2) • Softest intensity in pressure = 20 microPascals • Question is: What is the pressure for a sound that is 60 dB above threshold? • So: • For pressure: 60 = 20 log (Pressure/20x10-6) • 60/20 = log (Pressure/20x10-6) • 103 = Pressure/20 x 10-6 • Pressure = 103 * 20 x 10-6 • Pressure = 20,000 microPascals • Pressure = 0.02Pascals

  17. dB SPL vs. dB SL • dB SPL (sound pressure level) • the reference = 20 Pascal • i.e., the softest sound that normal hearing adults can detect • dB SL (sensation level) • the lowest sound level that a subject can detect

  18. bel = log (I1/I2) decibel (dB) = 10 log (I1/I2) decibel (dB) = 20 log (p1/p2)

  19. SPL Sound pressure level (SPL) uses 20 Pa as reference.

  20. Sound transmission • Sound decays as a function of distance. • I  Power/(4r2)  pressure2 • Sound intensity (I) is inversely proportional to distance from the sound source squared (r2 ). • Sound pressure (p) is inversely proportional to distance from the sound source (r ). • For each doubling of the distance, sound pressure level decreases by a factor of 2, or, 6 dB.

  21. mass reactance stiffness reactance FRICTIONresistance Interference Impedance - a measure of total opposition to energy flow Z = sqrt([R2 + (Xm - Xs)2] (R=resistance (friction); Xm=massreactance; Xs=stiffnessreactance)

  22. The impedance of any medium is called the characteristic impedance (Zc) of the medium • Zc = 0c (characteristic impedance) • I = p2/0c = p2/ Zc (p= rms pressure) 0 - density of the medium;c – speech of sound

  23. Interference When sound reflects of a wall, the reflected wave may encounter other waves from the source and destructive (or constructive) interference may occur. Figure 3.5

  24. Sound Shadow A sound shadow occurs when the size of the object is about that of a wavelength (c). Otherwise, the sound reflects from the object (b) or passes over it (c). In (c ) if this object is your head, the effect is called: Head shadow effect Figure 3.6

  25. Sound fields • Sound field: an environment that contains sound • Free field: a sound field with no reflections • Diffuse field: sound intensity is uniform throughout the room • Echoic room: a room with reflections • Anechoic chamber: use materials and shapes that absorb rather than reflect sound

  26. Reverberation time • The time it takes for the reverberant sound in a room to reach one thousandth or -60 dB of its original pressure. • 20 x log(1/1000) = 20 x (-3) = - 60 dB • RT  Vol / Ab Vol: room volume, Ab: total room absorption • Room absorption is related with the materials and shapes that made of the wall of the room

  27. Problems for chapter 3(15 min classroom activity) • Explain how a vibrating object sets up regions of condensation and rarefaction in the air. • Suppose the speed of sound is 400 m/s. What is the wavelength of a 1000-Hz tone? • Suppose your inter-aural distance is 17 cm. What is the frequency of a sinusoid that has a wavelength equal to your inter-aural distance? (c=340 m/s) • Suppose someone can only hear a pure tone at 4000 Hz with sound pressure >= 4000 µPa. What is his/her threshold in dB SPL for that frequency? • Mr. A is sitting 2 m away from a fan, and the sound pressure level at Mr. A is 60 dB SPL. If Mr. B is sitting 4 m away from the fan, what is the sound pressure level there? • What are the three components of impedance?

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