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PROGRESSIVE WAVES
PRESENTER:
1) SITI AMIRA BT ABDULLAH (DEHS)
2) NUR ASHIKIN BINTI CHE ALIAS ( DEHS)
3) NUR SHAHIRAH BINTI ZOLKIFLI ( DEHS)
4) NIK NUR FARHANA BINTI NIK MOHAMAD ( DBLT)
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SUMMARYa)DEFINITION
b)PARAMETERS
c)EQUATIONS
d)EXAMPLE QUESTION
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DEFINITIONS
~ Progressive waves distribute energy from a point source to a surrounding area. They move energy in the form of vibrating particles or fields.
TRANSVERSE
WAVE
LONGITUDINAL WAVES
~ Two types of progressive waves:
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TRANSVERSE WAVES:
• The waves propagates in the direction perpendicular to the direction of vibration of particles.
• The waves propagates in the form of crests and troughs.
• Example of transverse waves: vibration of a string, light, water.
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LONGITUDINAL WAVES:
• The waves propagates in the direction parallel to the direction of vibration of particles.
• The waves propagates as compressions and rarefactions.
• Example of longitudinal waves: sound waves and earthquake waves.
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WAVES PARAMETERS:
1) AMPLITUDE, A
• The maximum displacement of the vibrating particle from the equilibrium position.
• S.I unit: m
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2) PERIOD, T
• The time taken to complete one full cycle
• S.I unit: s
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3) FREQUENCY, f
• The number of cycle per unit time, f=1/T
• S.I unit: or Hz
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4) ANGULAR FREQUENCY, Ѡ
• Ѡ = = 2
• S.I unit:
h h𝑖𝑔 𝑒𝑟 𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 , h𝑠 𝑜𝑟𝑡𝑒𝑟 𝑝𝑒𝑟𝑖𝑜𝑑 (𝑇 )
𝑙𝑜𝑤𝑒𝑟 𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 , 𝑙𝑜𝑛𝑔𝑒𝑟 𝑝𝑒𝑟𝑖𝑜𝑑 (𝑇 )
Time, s
position
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5) WAVE LENGTH, λ
• The length along the direction of propagation between two corresponding point at the same phase.
• S.I unit: m
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6) WAVE NUMBER, k
• k=
• S.I unit: rad
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7) PHASE
• A and B = in phase
• B and C = in anti phase
• Phase difference = φ
• Calculating φ for x1 and x2
• φ = ( x1- x2)
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THE WAVE EQUATIONS• Wave moving in +x axis (forward) direction
y(x, t) = A sin (ωt- kx + φ)
Or y(x,t) = A sin (kx- ωt+ φ)
• Waves moving in x-axis (backward) direction.y( x,t) = A sin (ωt+ kx + φ)
Or y(x,t) = A sin (kx + ωt + φ)
Note:
A = amplitude, ω= angular frequency, k= wave number, φ= phase angle.
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VELOCITY OF PARTICLES
VELOCITY OF PROPAGATION
• The distance per unit time made by wave as it propagates in the medium.
• v= f λ
• Propagation velocity dependent on medium in which the waves propagates.
• Velocity in stretched string v=
where T = tension, μ =mass density= mass/ length
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GRAPHICAL REPRESENTATION OF WAVES
• Displacement – time graph (y-t)
y (x , t) = A sin (ωt – kx)
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• Displacement – distance graph (y-x)
y (x , t) = A sin (ωt – kx)
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EXAMPLE QUESTION
• The question of progressive wave is given asy = 0.3 sin (5)
Where x and y is in meter and t is in seconds.Determine its amplitude, frequency, wavelength, velocity, and wave direction.
Answer: y = O.3 sin (5)y = A sin (kx – ωt)
1) amplitude (A) = 0.3 mAngular frequency (ω) = 200Wave number (k) = 5
2) Wavelength, λk= 55λ= λ= 0.4m
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3) Angular frequency (ω) = ω = 200200T= T= 0.01 s 5) wave direction= backward
(-x-axis) frequency, f=
f= f=f= 100 Hz
4) Velocity v=f λ
f= 100 Hzλ= 0.4m
v= 100 = 100
The end