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:wavy_dash: WAVE MOTION :wavy_dash: - Coggle Diagram
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WAVE MOTION
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CHARACTERISTICS OF WAVE
wavelength
The distance from one peak to the next of a wave
λ = v/f
wave number
the number of waves per unit distance
k=2π/λ.
standing wave
Waves traveling in opposite directions can produce
standing waves
can be described by a sine function depending on position, with a time-varying amplitude
ET = Em cos wt sin kx
standing wave has crests and trough
wave crests
is the highest part of a wave,
wave trough
is the lowest part of a wave
:question: how to create standing waves :question:
when two sine waves of the same frequency, wavelength, and amplitude move in opposite directions
E1 = (Em/2) sin (kx - wt)
E2 = (Em/2) sin (kx + wt),
when first wave moves towards the right (positive x axis) and second wave moves towards the left (negative x axis)
frequency
is defined as one cycle per second
f = 1/T = ω/2π
WAVE MOTION
traveling waves
travelling waves
are the waves which travel from one medium to another
also known as progressive wave because they progress from one point to another
longitudinal waves
the medium to move parallel to the direction of the wave
transverse waves
the medium to move perpendicular to the direction of the wave
speed waves
the distance a wave travels in a given amount of time, such as the number of meters it travels per second
longitudinal waves
, the motion of particles takes place along x-axis and not along y-axis
transverse waves
, y denotes the movement of particles along y-axis.x denotes the direction of wave propagation in terms of x axis
Wave Speed V= ω/k whereω=angular frequency and k=wave number.
on a stretched string
the particles move up and down and the waves travel perpendicular to the oscillation of the particles
how transverse waves speed can be determine ?
mass per unit length, μ= m/l
tension, T
v= √(T/ μ)
Superposition Of Waves
Superposition And The Wave Equation
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The superposition principle states
that when two or more waves overlap in space, the resultant disturbance is equal to the algebraic sum of the individual disturbances.
:pencil2: Diagram:
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Wave Equation
If the wave is travelling to the left replace x-vt with x+vt
In each period, the wave travels one wavelength, λ
:check: v= λ/T= fλ
where,
v is velocity of waves
λ is wavelength
T is period
f is frequency
Interference Of Harmonic Waves
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Wave interference
is the phenomenon that occurs when two waves meet while traveling along the same medium.
:pencil2: The interference of waves causes the medium to take on a shape that results from the net effect of the two individual waves upon the particles of the medium.
:pencil2: Diagram:
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Constructive Interference
:unlock: Constructive interference is a type of interference that occurs at any location along the medium where the two interfering waves have a displacement in the same direction.
:unlock: In this case, both waves have an upward displacement; consequently, the medium has an upward displacement that is greater than the displacement of the two interfering pulses.
:pencil2: Diagram:
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Destructive Interference
Destructive interference is a type of interference that occurs at any location along the medium where the two interfering waves have a displacement in the opposite direction.
:pencil2: Diagram:
Superposition Of Standing Wave
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Standing waves
is a wave in which the amplitude at a given location does not vary with time.
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Standing wave patterns
are wave patterns produced in a medium when two waves of identical frequencies interfere in such a manner to produce points along the medium that always appear to be standing still.
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Antinodes
are points on a stationary wave that oscillate with maximum amplitude.
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Nodes
are points of zero amplitude and appear to be fixed.
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Examples of standing wave patterns:
:explode: First Harmonic Standing Wave Pattern
:explode: Second Harmonic Standing Wave Pattern
:explode: Third Harmonic Standing Wave Pattern
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Numerical Patterns Associated With Standing Wave Diagrams
Harmonic Analysis And Synthesis
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Fourier Synthesis:
The process of combining harmonics to form a complex wave.
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Fourier Analysis:
Determining the harmonic content of a complex wave.
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Harmonic Amplitudes for Sine, Triangle, Square, Sawtooth and Pulse
Wave Packet And Dispersion
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How to construct a wave packet?
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If several ways of different wavelengths (frequencies) and phase are superposed together, one would get a localized wave packet.
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Wave packet:
A group of waves with slightly different wavelengths interfering with one another in a way that the amplitude of the group (envelope) is non-zero only in the neighbourhood of the particle.
:pencil2: A wave packet is localized— a good representation for a particle!
