Ch15. Mechanical Waves
Liu UCD Phy9B 07 1 15-1. Introduction Wave pulse
Source: disturbance + cohesive force between adjacent pieces A wave is a disturbance that propagates through space Mechanical wave: needs a medium to propagate
Liu UCD Phy9B 07 2 Distinctions Wave velocity vs. particle velocity
Wave can travel & Medium has only limited motion Waves are moving oscillations not carrying matter along
What do they carry/transport? Disturbance & Energy
Liu UCD Phy9B 07 3 Types of Waves Transverse wave
Longitudinal wave
Liu UCD Phy9B 07 4 More Examples Transverse
Longitudinal
Transverse + Longitudinal
Liu UCD Phy9B 07 5 Sound Wave: Longitudinal
Liu UCD Phy9B 07 6 15-2. Periodic Waves
Liu UCD Phy9B 07 7 Continuous / Periodic Wave
Caused by continuous/periodic disturbance: oscillations
Characteristics of a single-frequency continuous wave
Crest / peak
Trough Wavelength: distance between two successive crests or any two successive identical points on the wave Frequency f: # of complete cycles that pass a given point per unit time Period T:1/f Liu UCD Phy9B 07 8 Wave Velocity
v=λ/T =λf Different from particle velocity Depends on the medium in which the wave travels Liu UCD Phy9B 07 9 15-3. Mathematical Description
Approach:
extrapolate motion of a single point to all points
from displacement, derive velocity, acceleration, energy…
Liu UCD Phy9B 07 10 Recall SHM: Position of Oscillator
cosθ=x/A θ=ωt ω - angular frequency (radians / s) = 2π/Τ = 2πf
x =Acosθ =Αcos ωt =Acos(2πt/Τ) Liu UCD Phy9B 07 11 Motion of One Point Over Time
Rewriting y as the particle displacement:
y
y =Αcos ωt =Acos(2πt/Τ)
Liu UCD Phy9B 07 12 Motion of Any Point at Any Time: Wave Function π For wave moving in +x direction x π y(x,t) = Acosω(t − ) Motion at x trails x=0 by a time of x/v v λ x t x x t y(x,t) = Acos 2 f (t − ) = Acos 2 ( − ) = Acos 2π ( − ) v T λ T π2 Wave number k = λ ω = vk y(x,t) = Acos(kx −ωt) For wave moving in -x direction y(x,t) = Acos(kx +ωt) Phase: kx±ωt
Liu UCD Phy9B 07 13 Example
Liu UCD Phy9B 07 14