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Physics 2c

Sound (chapter 17) Sound velocity “Donald Duck talk” Sound intensity Decibels Refraction & Reflection. Physics 2c. P and s are out of phase by 90 o or /2. Sound in gases. Spacial displacement amplitude s Pressure amplitude P. large +s. Min P. Max P. large -s.

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Physics 2c

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  1. Sound (chapter 17) Sound velocity “Donald Duck talk” Sound intensity Decibels Refraction & Reflection Physics 2c

  2. P andsare out of phase by 90o or /2. Sound in gases Spacial displacement amplitude s Pressure amplitude P large +s Min P Max P large -s

  3. P andsare out of phase by 90o or /2. Speed of Sound in gases  = Cp/Cv of the gas.

  4. How do different things sound? Frequency of sound determines our impression of it ! High frequency => high “pitch” Low frequency => low “pitch”

  5. Example: “Donald Duck talk” Wavelengths in human speech are set by geometry of human vocal chords & throat.  frequency of sound coming out of our mouth depends on speed of sound in vocal chord & throat.

  6. Question to Ponder: • Air: density = 1.2kg/m3; Cp/Cv = 7/5 • Helium: density = 0.17kg/m3; Cp/Cv = 5/3 • What’s f(air)/f(helium) for human speech? (a) roughly 1/3 (b) roughly 1/9 (c) roughly 3 (d) roughly 9 (e) roughly 1

  7. Sound Intensity • Determines the “loudness” of sound. • High intensity => “loud” • Low intensity => “quiet”

  8. Sound Intensity Force = pressure difference times area Work = Force times distance = ∆P · area · s Power = work/time =∆P · area · speed Intensity = Power/area = I s = displacement of gas

  9. Note: • Intensity of sound is a bit confusing because it depends on both the displacement amplitude s and the pressure amplitude ∆P . • We will show that the two are related, and equations can be built that depend on only one or the other!

  10. Following phase convention of figure 17-1 Note the phase difference! However, this equation requires knowledge of both pressure and displacement amplitude. Use F = m a to show that only one of the two needs to be known!

  11. Relating P and s via F=ma  Why this minus sign?

  12. Explaining the minus sign • X direction provides sign convention. • Force points from large to small pressure. P P+dP Force is negative iff P+dP > P dx

  13. Different expressions for Intensity • If air displacement amplitude is unknown: • If pressure amplitude is unknown:

  14. Human perception of sound intensity: “loudness” Given the wide range of sensitivity, it is natural to measure sound intensity on a logarithmic scale: Decibel

  15. Decibels I0 chosen as 1e-12 W/m2

  16. Question to ponder: • Assume the intensity drops by a factor 2. • What’s the change in decibel? (a) -1dB (b) -2dB (c) -3dB (d) -4dB

  17. How to calculate this: • Ratio of Iafter / Ibefore =1/2

  18. Sound in solids Bulk modulus of elasticity: B = -dP/(dV/V)

  19. Typical sound speedsat room temperature Air ~340 m/s Water ~1500 m/s Steel ~6000 m/s

  20. Reflection Reflection depends on boundary conditions. fixed end loose end

  21. Partial Reflection Partial reflection occurs at the boundary of different media. Reflected wave may be inverted depending on the characteristics of the two media.

  22. Rays, a short hand for drawing waves. Refracting plane wave. May be depicted as rays instead of showing the full wave pattern.

  23. Reflection & Refraction

  24. Refraction Refraction occurs at the boundary of different media. Refraction = change of wave direction. (for water waves in shallow water, wave propagation depends on water depth. A change in depth is thus a change in “media”.)

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