Another way to think of sound

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Presentation transcript:

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

Speed of Sound Restoring force inertia v =

Fractional volume change Sound in a Fluid Restoring force = pressure Pressure responds to deformation Bulk modulus B −Pressure change Fractional volume change −p DV/V0 B = = Units = pressure units = Pa

Sound in a Solid Rod Restoring force = tensile stress Stress = Force/Area (in one dimension) Strain = Fractional elongation Young’s modulus Y Longitudinal stress Longitudinal strain Y = F/A DL/L0 = Units = N/m2 = Pa

Group 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.

Group Work / CPS 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?

Group Work / CPS 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. ?

Group Work / CPS For a sound wave: What is the particle acceleration where the pressure excursion is greatest? A. Maximum. B. Zero. C. ?

Longitudinal Wave Formula y(x, t) = A cos(kx − wt) y = displacement from equilibrium position x Particle position = x + y

Longitudinal Wave Pressure y(x, t) = A cos(kx − wt) Find an expression for pressure excursion p(x, t) In a fluid, p = − bulk modulus fractional volume change What is the fractional volume change of a segment of the fluid?

Longitudinal Wave Pressure Does the net force on a segment really relate to the pressure gradient?

Lab 12 Ignore the question on p. 112 Replace Postlab question 5 with: Calculate Young’s modulus Y for brass, steel, and aluminum from the literature values of density and speed of sound. Compare these to the literature values of Y for these materials. The values are substantially different! What might these differences mean?