Waves
Waves
A wave is a moving disturbance that
transports energy without transporting
matter
–
Parts of the string move – kinetic
energy
–
String stretches – potential energy
Some waves (mechanical) require a medium,
others don't.
The wave propagates along the direction of
wave motion
Waves can be transverse or longitudinal
depending on the direction of disturbance
relative to the direction of propagation
Quantification
Some waves a periodic (in time
and space).
Use SHM: y end = A sin (2 π f t )
2π x
y= A sin (2 π f t − λ )
λ is the wavelength, the distance
between adjacent troughs or
crests.
Speed of a Wave
v = λ =f λ
1/ f
Δx λ
v=
=
Δt T
v depends on the medium (or lack of) and type of wave.
Not on f or λ!
Example: Wave on a string. Wave will be faster in
lighter, tauter (depends on Tension) string.
√
FT
v string wave = μ
where, μ is the mass/length and FT is the tension force.
Sound
Sound is a type of longitudinal mechanical wave
(it requires a medium).
Speed of sound in air 343 m/s.
Sound can travel through other substances.
Waves in Solids
Sound and other waves can travel in solid
objects.
Any longitudinal wave will move the same
way a sound wave would.
√
Y
v long , solid = ρ
Transverse waves are allowed because
when a solid experiences a shearing
force, there is a restorative force that
leads to the oscillation motion
associated with a wave.
Because of flow issue, no transverse
waves in bulk fluids (liquid or gas)
Other Types of Waves
Electromagnetic – visible light, radio waves, microwaves, x
rays, infrared, ultraviolet, gamma rays. Require no
medium. Transverse waves.
Water waves – Both transverse and longitudinal.
Spherical and Plane Waves
power
I=
area
P
I=
2
4πr
I∝A
2
Amplitude
I is uniform
Superposition
When two (or more) waves are
present, the disturbance is
equal to the sum of the
disturbance of the individual
waves.
This gives rise to interference.
“Interference” is misleading since
the waves won't actually affect
each other.
Interference
Periodic Waves and Interference
Damping
Driven Oscillator