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 distances BUT particles in medium through which wave travels move only a small amount

Conceptual Example Is the velocity of a wave moving along a cord the same as the velocity in the cord? NO!!

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.

Wave velocity v  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

 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 F T : v = [F T /(m/L)] ½ Example 11-11

Sect. 11-8: Longitudinal & Transverse Waves

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

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 F T : v = [F T /(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

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

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)kA 2  Energy in wave  (wave amplitude) 2 Define: Intensity of wave I: I  (Power)/(Area) = (Energy/Time)/(Area)  I  A 2

Spherical Waves

Intensity of spherical wave:I  (1/r 2 )  (I 2 /I 1 ) = (r 1 ) 2 /(r 2 ) 2 Also: I  A 2  AmplitudeA  (1/r)  (A 2 /A 1 ) = (r 1 )/(r 2 ) Example 11-13