Chapter 16 Flashcards
The phase constant
π₯(π‘)=π΄ cosβ‘(ππ‘+π)
Phase constant for y-π
π¦(π)=π΄ cosβ‘γ(π)γ
Phase constant for y-π
π¦(π₯)=π΄ cosβ‘γ(π+π)γ
Phase constant for x-t if π=0
π₯(π‘)=π΄ cosβ‘γ(ππ‘)γ
Phase constant x-t if π>0
π(π) means x-t
βx-position as a function of timeβ
π(π) means (x-t graph)
βx-position as a function of timeβ
π(π) means
(x-t graph)
βy-position as a function of π-positionβ
π[π] on a graph axis, means (x-t graph)
y-position measured in meters
Wave motion β snapshot (photograph) when?
We take a snapshot (a photograph) and we get a graph of π¦-POSITION versus π₯-POSITION.
If π meters is the distance for one cycle, write the mathematical expression for this graph
π the spring constant equation
(remember is different then for wave number)
π the wave number equation
(remember it is different then spring constant)
π the wave number equation
(remember it is different then spring constant)
Waves β snapshot general equation
π¦(π₯)=π΄ cosβ‘γ(ππ₯)γ= π΄ cosβ‘(2π/π π₯)
What is the equation using this graph? and the wavelenght?
π¦(π₯)=2 cosβ‘γ(2π₯)γ
π=π π
Tranverse Wave Motion: The relationship between particle and wave
Wave Speed
The General Wave Equation
π¦(π₯,π‘)=π΄sin(ππ₯Β±Οπ‘+π)
Do you remember, for a mass-spring system, we had two expressions (equations) for the angular frequency, π
, the speed of a wave can be written in terms of properties of the wave, and properties of the medium/material
Linear mass density:
Centripetal acceleration to the centre of the circle
The power of a wave on a rope/wire/string:
The power of a wave on a rope/wire/string:
Definition of intensity:
Definition of intensity:
Surface area of a sphere
Surface area of a sphere
two interfering waves of the same frequency, wavelength and amplitude
Summation of the displacement of two waves, y1 and y2 that propagate in opposite directions
Resultant wave equation
π²^β² (π±,π)=π²_π (π,π)+π_π (π,π)
Resultant wave equation
π²^β² (π±,π)=π²_π (π,π)+π_π (π,π)
What can you think of this term as?
as the amplitude of the snapshot
What is the red underlined mean?
Effective Amplitude of sinβ‘(ππ₯)
Standing waves: Resonance
How did they get here?
