1
Wave phenomena
Waves show reflection, refraction,
diffraction and interference.
The reflection, refraction and dispersion of
waves can be explained by Huygen’s
principle.
Huygen’s principle (Essay)
Every point on a wavefront may be regarded as a source
of secondary spherical wavelets which spread out with
the wave velocity.
The new wavefront is the envelope of these secondary
wavelets.
Secondary
source
Constructed
wavefront
Constructed
wavefront
First position of
wavefront
First position
of wavefront
Secondary
wavelet
simulation
Explanation of law of reflection by
Huygen’s principle
Secondary wavelet
from A
Incident
wavefront
Reflected
wavefront
r
i
a
b
Consider DAA’B’ and DB’BA.
AA’ = BB’ (provided)
AA’B’ = ABB’ = 90o
AB’ = AB’ (common side)
DAA’B’  DB’BA (R.H.S.)
a = b (corr. ,  D)
∵ i = a, a = b and b = r
∴ i=r
(law of reflection)
Explanation of law of refraction by
Huygen’s principle
Incident wavefront
i
a
b
Consider DAA’B’ and DABB’
BB '
sin a AB BB ' v1t v1




sin b AA' AA' v 2 t v 2
AB
Medium 1
∵ i = a and r = b
Medium 2
r
Refracted wavefront
Secondary wavelet from A
sin i v1
 (constant)
∴
sin r v2
(Snell’s law)
the constant is called the refractive index, 1n2
for waves passing from medium 1 to medium 2.
Explanation of dispersion by Huygen’s
principle
If the speed of waves in a given medium
depends on the frequency of the waves, the
medium is called a dispersive medium.
Vacuum is a non-dispersive medium since the
velocity of light for different colours (or
frequencies) in vacuum is the same.
Glass is a dispersive medium because when
white light enters glass, the velocity is not the
same for different colours (or frequencies).
Dispersion
Waves of frequency f1 and f2
travelling with same speed
White light
Blue wavefront
Medium 1
Medium 2
Red wavefront
The secondary wavelet of blue light travels slower than that of
red light in glass. Blue light is refracted more than red light
and the refracted waves travel in slightly different direction.
This phenomenon is called dispersion
Reflection of a longitudinal pulse
compression
rarefaction
compression
rarefaction
Explanation
Equilibrium positions
compression
rarefaction
displacement
Direction of wave
compression
distance
- ve
slope
+ ve slope
- ve
slope
displacement
Direction of wave
distance
With a phase change of p
(compression  compression)
Explanation
Equilibrium positions
compression
rarefaction
displacement
Direction of wave
compression
distance
- ve
slope
+ ve slope
- ve
slope
displacement
Direction of wave
distance
No phase change
(compression  rarefaction)
Application of reflection
P1 P2
t
Radar
aerial
Radar (radio detection and ranging)
Employs microwaves (e.g. 3 cm microwaves )
The distance d of the object can be calculated from the
time lag t between the transmitted pulse P1 and the
reflected pulse P2 by the equation d = 2ct where c is the
speed of light.
Distance of the object is determined form the time lag t
Size of the object is determined by the strength of
reflected waves.
Sonar (sound navigation
and ranging)
Employs ultrasonic waves.
i.e. waves with f > f audible
transmitter
(20kHZ)
ultrasound waves
Submarines use sonar to
produced by a sonar
keep track of water depth.
echo
Fishing vessels use sonar to
spot shoals of fish.
Reasons for using ultrasound
rather than audible sound
Less diffraction so that the wave is more
concentrated and can penetrate to a
greater depth.
Not be interfered by the audible sound in
the sea.
Smaller objects can be located.
Reflection of transverse waves
• video
Refraction
Example 2
60o
i
a
b
d
r
60o
60o
60o
• If i = 70o, find the angle of
deviation d.
• By symmetry, i = r, a = b.
• By geometry, d = a + b --- (1) and
• (i – a) + (r – b) = 60o --- (2)
• By Snell’s law,
sin i = n sin (i – a) --- (3)
• Sub (1), (2) and (3)
• sin i = n sin 30o
• sin 70o = n sin 30o
• n = sin 70o / sin 30o = 1.879
• a + 30o = 70o
• a = 40o
• angle of deviation d = 2a = 80o
Real depth and apparent depth
r
apparent depth
D’
C
O
image r
B
i
i
objec
t
A
nwater
real depth D

apparent depth D'
• Suppose a fish is at A
but it is image is at B
which is nearer to water
surface.
• AC is called the real
real
depth and BC is the
depth D
apparent depth.
CO
 (1)
D
CO
tan r 
 (2)
D'
sin r tan r
nwater 

sin i tan i
(2)
tan r D


(1)
tan i D'
tan i 
Superposition
Two pulses on a string
approaching each other.
The resultant displacement of
the string is the sum of the
individual displacements. i.e.
the pulses superpose(疊置) .
A large pulse is produced.
After crossing, each pulse
travels along the string as if
nothing had happened and it
has its original shape.
Principle of Superposition
Pulses (and waves), unlike particles, pass
through each other unaffected.
The resultant displacement is the vector
sum of individual displacements due to
each pulse at that point
• Superposition can be used to find the resultant (solid line)
of two waves (dotted line) of different wavelength and
amplitude.
displacement
1.5
1
0.5
0
-0.5
-1
-1.5
A
B
P
C
Q
D
R
S
distance
Example 2
Two pulses are traveling toward each other, each at 10 cm s-1 on a
long string.
Sketch the shape of the string in the following at t = 0.6 s.
Solution:
Distance travelled by each pulse = vt = (10)(0.6) = 6 cm
1 cm