1. Pressure Waves Another way to think of sound § 16.1–16.2

2. Group Poll For any wave/oscillation: –What is the particle speed when the displacement magnitude is greatest? A. Maximum.B. Zero. C. ? –What is the displacement magnitude when the particle speed is greatest? A. Maximum.B. Zero. C. ?

3. Group Poll For any wave/oscillation: –What is the particle acceleration when the particle speed is greatest? A. ±Maximum.B. Zero. C. ? –What is the particle speed when the particle acceleration is greatest? A. Maximum.B. Zero. C. ?

4. Longitudinal Wave Formula y(x, t) = A cos(kx –  t) y = displacement from equilibrium position x Particle position = x + y What phase has greatest displacement? What phase has greatest acceleration? What phase has greatest speed? What phase has greatest density?

5. Longitudinal Waves 0 1/8 T 2/8 T 3/8 T 4/8 T 5/8 T 6/8 T 7/8 T Where are the crests? Where are the troughs?

6. Board Work Draw several cycles of a longitudinal wave train. –What force accelerates the particles? –Identify where pressure is high or low. –Identify the acceleration directions at different positions along a phase.

7. Group Poll For a sound wave: –What is the pressure excursion where the particle acceleration is greatest? A. Maximum.B. Zero. C. ? –What is the particle acceleration where the pressure excursion is greatest? A. Maximum.B. Zero. C. ?

8. Speed of Sound v = Stiffness Inertia

9. Sound in a Fluid Restoring force: pressure gradient Bulk modulus B (stiffness) Units = pressure units = Pa –Pressure change Fractional volume change –p–p V/V0V/V0 B == Pressure responds to deformation

10. Longitudinal Wave Pressure y(x, t) = A cos(kx –  t) What is the  V/V 0 of a segment of the fluid? Find an expression for pressure excursion  p(x, t)  p = –B VV V0V0  p(x, t) = BAk sin(kx –  t)

11. Speed of Sound in a Gas B =  p 0 p 0 = nRT V0V0 density  0 = m V0V0 nM V0V0 = n V0V0 00 M = so p 0 =  0 RT/M v = B/0B/0 M  RT = n = number of moles R = gas constant T = absolute temperature M = molar mass

12. m/s

13. Sound in a Solid Rod Restoring force: tension gradient Stress = Force  /Area (in one dimension) Strain = Fractional elongation Young’s modulus Y (stiffness) Units = N/m 2 = Pa Longitudinal stress Longitudinal strain Y = F/AF/A L/L0L/L0 =