Waves - I Flashcards
Mechanical waves
Move through a medium
Ex: water waves, sound waves, seismic waves
Electromagnetic waves
Light
Ex: x-rays, UV, IR
*don’t require a medium to propagate
Matter Waves
Quantum mechanical description of nature
Describes physical world at short length scale, like molecules for example
Transverse waves
The disturbance is perpendicular to the wave’s direction of travel
Slinky ex: your hand is moving up and down as the wave is traveling right wards
Ex: waves on string, water waves
Longitudinal waves
The disturbance is PARALLEL to the direction of propagation
Slinky ex: your hand is moving left and right and so is the wave — you’re pushing onwards and out
Ex. Sound waves
Traveling waves
Waves that move from one point to another (transverse and longitudinal)
Wave function y = y(x,t) = h(kx+ωt) plus or minus
Sinusoidal Waves
Wave forms are described sine and cosine functions
y(x,t) = ym sin(kx- ωt)
ym
Amplitude = Max displacement
λ and κ
Wave length and Angular wave number:
Describes spatial dependence
k = 2π/λ
T, f, ω
Period, frequency, angular frequency: describe TIME dependence
ω = 2πf/T
φ
Phase constant: gives displacement at x = 0 and t = 0
Necesita para describir una ola genérica
y(x,t) = ym sin(kx+ ω + φ) *+/-
Relationship between λ & κ
If POSITION changes by one wavelength, the the displacement should not change
Relationship between T and ω
If TIME changes by one period, the the displacement should not change
ω=2π/T
Speed of waves
Mesures how fast the pattern (shape) moves
Measured by following a point retaining its displacement
Sinusoidal waves
A point retaining displacement has a constant phase
Sinusoidal waves
A point retaining displacement has a constant phase.
y (x, t) = ym sin (kx − ωt) = (constant)
⟹ kx − ωt = (constant)
⟹ v =ω/k = λ/T = fλ
y(x,t) = ym sin(kx+ ω) function is moving in the
negative direction
Relationship between tension and wave speed
greater tension, the faster the wave travels
- the speed INCREASES as the tension, 𝜏 INCREASES
Inertial property of a rope
the wave travels faster on a lighter rope
Relationship between wave speed and linear mass density
the speed DECREASES as the linear density μ =M/L, INCREASES
Wave speed on a stretched string
v = the square root of (τ/μ)
Transverse speed (u)
measures how fast elements of a medium move in the oscillation direction
u = ∂y/∂t = − ωym cos (kx − ωt)
Kinetic Energy
dK =1/2dmu^2 =1/2μdxω^2y^2mcos^2(kx − ωt)
Transport of Kinetic Energy
(dK/dt)avg = 1/4 μvω^2y^2m
An oscillating system
(KE) = (PE)
Total Average Power
Pavg = 1/2μvω^2y^2m
Principle of Superposition
Overlapping waves algebraically add to produce a net wave.
Overlapping waves do not alter motion of each other
Standing Waves
If two waves with the same amplitude and frequency travel in opposite directions, their
interference produce a standing wave
Exactly in phase wave
produces a large resultant wave – a big wave
Exactly out of phase wave
produces a flat string
Node
a point with zero amplitude
Antinode
a point with a maximum amplitude
Fixed boundary
reflected wave is inverted
Free boundary
reflected wave is not inverted
Resonance
A standing wave pattern (oscillation mode) can be produced
only for certain frequencies (resonant frequencies).
Resonant frequency
L = nλ/2 where λ =2L/n f = n(v/2L)
