1) The document defines transverse and longitudinal waves, and discusses key wave parameters such as amplitude, period, frequency, wavelength, phase, and velocity. 2) It provides equations for transverse wave motion and defines related concepts like angular frequency, wave number, phase difference, and graphical representations of waves. 3) An example question is given and solved to determine the amplitude, frequency, wavelength, velocity, and propagation direction of a progressive wave defined by the equation y = 0.3 sin (5πx + 200πt).

1. 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)

2. SUMMARY
a)DEFINITION
b)PARAMETERS
c)EQUATIONS
d)EXAMPLE QUESTION

3. 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:

4. 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.

5. 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.

6. WAVES PARAMETERS:
1) AMPLITUDE, A
• The maximum displacement of the vibrating particle from the equilibrium
position.
• S.I unit: m

7. 2) PERIOD, T
• The time taken to complete one full cycle
• S.I unit: s

8. 3) FREQUENCY, f
• The number of cycle per unit time, f=1/T
• S.I unit: 𝑠−1 or Hz

9. 4) ANGULAR FREQUENCY, Ѡ
• Ѡ =
2𝜋
𝑇
= 2𝜋 f
• S.I unit: 𝑟𝑎𝑑 𝑠−1
ℎ𝑖𝑔ℎ𝑒𝑟 𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦, 𝑠ℎ𝑜𝑟𝑡𝑒𝑟 𝑝𝑒𝑟𝑖𝑜𝑑 𝑇
𝑙𝑜𝑤𝑒𝑟 𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦, 𝑙𝑜𝑛𝑔𝑒𝑟 𝑝𝑒𝑟𝑖𝑜𝑑 𝑇
Time, s
position

10. 5) WAVE LENGTH, λ
• The length along the direction of propagation between two corresponding
point at the same phase.
• S.I unit: m

11. 6) WAVE NUMBER, k
• k=
2𝜋
λ
• S.I unit: rad 𝑚−1

12. 7) PHASE
• A and B = in phase
• B and C = in anti phase
• Phase difference = φ
• Calculating φ for x1 and x2
• φ =
2𝜋
λ
( x1- x2)

13. 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.

14. VELOCITY OF PARTICLES
• 𝑣 𝑦 =
𝑑𝑦
𝑑𝑥
= 𝐴ω sin(ω𝑡 − 𝑘𝑥 + ϕ)
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= 𝑇/μ
where T = tension, μ =mass density= mass/ length

15. GRAPHICAL REPRESENTATION OF WAVES
• Displacement – time graph (y-t)
y (x , t) = A sin (ωt – kx)

16. • Displacement – distance graph (y-x)
y (x , t) = A sin (ωt – kx)

17. EXAMPLE QUESTION
• The question of progressive wave is given as
y = 0.3 sin (5𝝅𝒙 + 𝟐𝟎𝟎𝝅𝒕)
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 (5𝜋𝑥 + 200𝜋𝑡)
y = A sin (kx – ωt)
∴ 1) amplitude (A) = 0.3 m
Angular frequency (ω) = 200𝜋
Wave number (k) = 5 𝜋
2) Wavelength, λ
k=
2𝜋
λ
5𝜋 =
2𝜋
λ
5𝜋λ = 2𝜋
λ=
2𝜋
5𝜋
λ= 0.4m

18. 3) Angular frequency (ω) =
𝟐𝝅
𝑻
ω =
2𝜋
𝑇
200𝜋 =
2𝜋
𝑇
200𝜋𝑇 = 2𝜋
T=
2𝜋
200𝜋
T= 0.01 s 5) wave direction= backward
(-x-axis)
∴ frequency, f=
𝟏
𝑻
f=
1
𝑇
f=
1
0.01
f= 100 Hz
4) Velocity
v=f λ
f= 100 Hz
λ= 0.4m
v= 100 × 0.4
= 100