Sect. 11-7: Wave Motion (Lab!)

1. Sect. 11-7: Wave Motion (Lab!) • Various kinds of waves: • Water waves, Waves on strings, etc. • Our interest here is in mechanical waves. • Particles of matter move up & down or back & forth, as wave moves forward. • General feature: • Wave can move over large distancesBUTparticles in medium through which wave travels move only a small amount

2. Conceptual Example 11-10 • Is the velocity of a wave moving along a cord the same as the velocity in the cord? NO!!

3. Waves require a medium though which to propagate. • Waves carry energy (through the medium). • The energy must come from some outside source. • The source is usually a vibration (often a harmonic oscillation) of the particles in the medium. • If the source vibrates in SHM, the wave will have sinusoidal shape in space & time: • At fixed t: Position dependence is sinusoidal • At fixed position x: Time dependence is sinusoidal.

6. Wave velocityv  velocity at which wave crests (or any part) move. v  particle velocity. Period :T = time between crests. Frequency:f = 1/T Wavelength:λ = distance between crests  λ = vT or v = λf

7.  v = λf or λ = vT • Frequency f & wavelength λ depend on properties of the source of the wave. • Velocity v depends on properties of medium: String, length L, mass m, tension FT: v = [FT/(m/L)]½ • Example 11-11

8. Sect. 11-8: Longitudinal & Transverse Waves

9. Longitudinal Waves Sound waves: Longitudinal mechanical waves in a medium (shown in air) Still true that v = λf or λ = vT

11. For longitudinal & transverse waves we always have: v = λf or λ = vT • As for waves on string, the velocity v depends on properties of the medium: String, length L, mass m, tension FT: v = [FT/(m/L)]½ Solid rod, density ρ, elastic modulus E(Sect. 9-5):v = [E/ρ]½ Liquid or gas, density ρ, bulk modulus B(Sect. 9-5):v = [B/ρ]½ • Example 11-12

12. Water waves: Surface waves. A combination of longitudinal & transverse:

13. Sect. 11-9: Energy Transport by Waves • For sinusoidal waves: Particles in the medium move in SHM, amplitude A. From SHO discussion, we know:  E = (½)kA2  Energy in wave  (wave amplitude)2 • Define: Intensity of wave I: I  (Power)/(Area) = (Energy/Time)/(Area)  I  A2

14. Spherical Waves

15. Intensity of spherical wave: I  (1/r2)  (I2/I1) = (r1)2/(r2)2 • Also: I  A2  Amplitude A  (1/r)  (A2/A1) = (r1)/(r2) • Example 11-13