transverse wave, motion in which all points on a wave oscillate along paths at right angles to the direction of the wave's advance. Surface ripples on water, seismic S (secondary) waves, and electromagnetic (e.g., radio and light) waves are examples of transverse waves.

1. Transvers waves
and analysis

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3. Mechanical Waves
– A mechanical wave is a wave that is an oscillation/vibration of matter, and
therefore transfers energy through a medium.
– For example water waves, sound waves, and seismic waves.

4. PROPERTIES
Mechanical waves transport energy
This energy propagates in the same direction as
the wave.
Mechanical waves can be produced only in media
which possess elasticity and inertia.
A mechanical wave requires an initial energy
input.

5. Transverse wave
– It is the form of wave in which particles of medium vibrates about their mean
position perpendicular to the direction of motion of wav
Ϥ(x,t) = 𝑒
+
𝑖𝜔𝑡(𝑡−
𝑥
𝑣
)
𝑎𝑦 = -ω2y
𝑎𝑦=0
𝑣𝑦 𝑚𝑎𝑥 =-ωA
𝑣𝑦=0
𝑎𝑦 𝑚𝑎𝑥= - ω2A
𝑣𝑦
A
x =0
V
propagational
velocity
λ
X
Y
Y(x,y) =Asin
2𝜋
λ
(x-vt)
𝑣𝑦=
𝑑𝑦
𝑑𝑥
= 𝜔Acos
2𝜋
λ
(x-vt)
𝑎𝑦(x,y) =
𝑑𝑦
𝑑𝑥
2
= -
𝜔2
𝑦 −𝜔2
𝑦= −𝜔2
Asin
2𝜋
λ
(x-
vt)

6. 𝜕2𝑦
𝜕𝑥2 =
1
𝑣2
𝜕2𝑦
𝜕𝑡2
Ϥ(x,t) = 𝑒
+
𝑖𝜔𝑡(𝑡−
𝑥
𝑣
)
Transvers waves on a string C =√
𝑇
𝑚
Transvers ripples on a pond C = √
πσ
λρ
Plane Wave Equation
For Transvers Wave Equation
Speed For Different Transvers Waves

7. Longitudinal wave
– Longitudinal waves cause the medium to vibrate
parallel to the direction of the wave.
– It consists of multiple compressions and rarefactions.
– The rarefaction is the farthest distance apart in the
longitudinal wave
– The compression is the closest distance together
– For example sound waves

8. Ϥ(x,t) = 𝑒
+
𝑖𝜔𝑡(𝑡−
𝑥
𝑣
)
𝜕2𝑦
𝜕𝑥2 =
1
𝑣2
𝜕2𝑦
𝜕𝑡2
Longitudinal waves on a spring C =√
𝑘𝐿
𝑚
Longitudinal waves on a rod C = √
𝐸
ρ
Sound wave in a gas C = √
Υ𝑝
ρ
Plane Wave Equation
For Longitudinal waves
Speed For Different Longitudinal Waves

9. Surface waves
– This type of wave travels along the surface or interface between two media.
– waves in a pool, or in an ocean, lake
– Rayleigh waves, also known as ground roll, are waves that travel as ripples with
motion similar to those of waves on the surface of water.