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)

SUMMARYa)DEFINITION

b)PARAMETERS

c)EQUATIONS

d)EXAMPLE QUESTION

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:

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.

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.

WAVES PARAMETERS:

1) AMPLITUDE, A

• The maximum displacement of the vibrating particle from the equilibrium position.

• S.I unit: m

2) PERIOD, T

• The time taken to complete one full cycle

• S.I unit: s

3) FREQUENCY, f

• The number of cycle per unit time, f=1/T

• S.I unit: or Hz

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

5) WAVE LENGTH, λ

• The length along the direction of propagation between two corresponding point at the same phase.

• S.I unit: m

6) WAVE NUMBER, k

• k=

• S.I unit: rad

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)

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.

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

GRAPHICAL REPRESENTATION OF WAVES

• Displacement – time graph (y-t)

y (x , t) = A sin (ωt – kx)

• Displacement – distance graph (y-x)

y (x , t) = A sin (ωt – kx)

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

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