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

2. Speed of Sound
Restoring force
inertia
v =

3. 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

4. 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

5. 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.

6. 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?

7. 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. ?

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

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

10. 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?

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

12. 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?