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3 : WAVE MOTION - Coggle Diagram
3 : WAVE MOTION
1 Characteristic :
simple harmonic motion as a oscillator
ex. wave motion produced by oscillator,
frequency of wave motion = frequency of oscillator
began with vibration(come from SHM)
amplitude oscillator ≠ amplitude of wave
2 Type of waves; Tranverse
its perpendicular to the
oscillator
when the velocity high, the tension also high
when the mass is high. the tension becomes low
Longitudinal
have compressor & expansion
The velocity on elastic restoring force of a medium:
4 Mathematical represent of travelling wave *
D(X) = A sin (2π/λ) x
D(X) equal to x = Acos (wt + ϕ)
(2π/λ) x = k, k= 2π/λ, w= 2πf
3 Energy transported by waves
E= 1/2 k A^2 = 2π^2 mf^2A^2d
A is amplitude, K is number of waves
if same density,
I = P/S = 2π^2vρf^2A^2
I is intensity(power) S is surface area
5 The wave equation
6 the principle of superposition
:
SUPERPOSITION
the displacement at any point is the vector sum of the displacements of all waves passing trough that point at that instant
FOURIER'S THEOREM : any complex periodic wave written as the sum of sinusoidal waves of different amplitude,frequencies and phases
INTERFERENCE
the superposition principle says that when two waves pass through the same point, the displacement is the arithmethic sum of the individual displacements
added destructively
the add constructively
non-identical waves exhibits both constructive and destructive interference
7 reflection and transmission
Reflection of waves is the change in the direction of a wave upon striking the interface between two materials.
When a wave strikes any interface between any two mediums the bouncing back of wave is termed as reflection of waves.
Open boundary: - When a wave strikes an interface in case of open boundary it will get reflected as well as refracted.
Closed boundary or a rigid boundary: - When a wave is incident on an interface it will completely get reflected. Example:-Wave striking wall(echo)
REFLECTION AT A RIGID BODY
The reflection at the rigid body will take place with a phase reversal of π or 180.
REFLECTION AT OPEN BOUNDARY
The reflection at an open boundary will take place without any phase change.
In this case at boundary pulse is generated.Therefore amplitude at the boundary is maximum.
This means the reflected wave and incident wave are in phase with each other.As a result the phase difference φ=0
Therefore, yi(x, t) = a sin (kx – ωt),
yr(x, t) = a sin (kx – ωt).
By superposition principle y= yi + yr =2a sin (kx – ωt)
