WAVES passing through a chosen point per second.

Therefore if 5 complete waves pass a chosen

What are Waves? point per second the frequency of the wave is 5
A wave can be defined as the transmission of vibrations per second or 5 Hz (hertz is the SI unit
energy or information from one point to for frequency). Similarly if 1 complete wave was
another. There are many different types of to pass through a chosen point per second the
waves which have different sets of frequency of that wave will be 1 Hz.
characteristics. A simple way of producing a
wave is attaching one end of a rope to a fixed
position and moving the other end in an upwards
and downwards manners. The energy applied in
an upward and downward manner or (direction
of vibration applied on the rope) causes the
wave to move in the direction of the fixed end of
the rope. This is known as a transverse wave. If
this same energy applied is 90° or at right angles
to the direction of the wave this is called a
The period (T) of a wave is the time taken for one
progressive transverse wave.
complete wave to be generated and can be
found using the formula T= 1/f where f is the
frequency of the wave.

The speed (v) of a wave can be defined as the

distance moved by a crest or any given point on
the wave in just 1 second. The speed can be
found using the wave equation v = f λ.
The distance between two successive crest or Where v is the speed of the wave, f is the
trough is called the wavelength and is frequency of the wave and λ is the wavelength.
represented by the Greek letter λ (lambda).

The amplitude (a) is the distance between the

heights of the crest or the depths of the trough
before the wave goes back to its position of rest
or zero displacement.

A displacement vs time graph shows how the

displacement of a vibrating object at a particular
distance along the wave varies with time. This
Frequency ( f ) of a wave can be defined as the introduces the phases of the wave know as
number of complete waves generated per positive phase.
second or the number of successive crests
The Wave Equation direction of travel of the waves and the
normal to the strip is 60o. Incident at other
angles shows that the angles of reflection
and incidence are always equal.

Given the graph above, suppose we have 3

waves passing every second, that gives us a Note that the angle between the wavefont
frequency of 3Hz, and the wavelength of the and the mental strip i is the same for the
waves are 20cm. We can use this to calculate the
angle i between the direction of travel of the
speed of the wave given the formula v= f λ.
waves and the normal to the strip and vice
i.e speed of wave = frequency X wavelength. versa, the angle between the wavefont and
the mental strip r is the same for the angle r
Therefore the speed of the wave is
between the direction of travel of the waves
v = 3Hz X 20cm = 60 cm s-1 and the normal to the strip.
Similarly if we have waves of frequency 10 Hz
with crests 5mm apart. The speed will be v= f λ =
10Hz X 5 mm = 50mm s-1. If the frequency is Refraction
reduced to 5Hz. What will be the distance
between crests? If we have a speed of 50mm s-1 {Refraction is the process of light waves
then λ= v/f = 50mm s-1 / 5Hz = 10 mm. bending towards the normal by passing
through a boundary that separates two
media. This is caused by the change in speed
experienced by a wave when it changes
Reflection
medium.}
Snell’s law n1 sin θ1 = n2 sin θ2
In water waves refraction occurs when
waves bend towards a normal via going
from a region of depth to a shallow region
and the waves in the shallow region
experiences a slower velocity than that of
Consider a ray of waves being reflected on a the waves in the deep region. This occurs
mirror. The angle of incident i.e. the angle i since the wavelength of the waves in the
between the direction of travel of the waves shallow region have shorter wavelength
and the normal to the strip is 60o. The angle than those in the deeper parts. Using the
of reflection i.e. the angle r between the equation v= f λ we can see that if the value
of the velocity decreases as the wavelength Diffraction
decreases.
The spreading of waves at the edge of
Sin θ1 / Sin θ2 = v1/ v2 = λ1/ λ2. obstacles.

Consider the images above to be taken in a

ripple tank. In images “a” & “b” straight
water waves are falling on gaps formed by
obstacles. The gap width in “a” is about the
same as the wavelength of the waves (about
1cm). Looking closely at the waves passing
through the gap we see they are circular and
spread out in all directions. The gap width in
“b” is way more when compared to the
wavelength of the wave (about 10cm).
Looking closely at the waves passing through
the gap we see some spreading occurring
but is less obvious. In images “c” & “d” a
single edge and single slit respectfully is seen
showing waves of different wavelengths.
Looking closely we see that longer
wavelengths gives more diffraction than
shorter ones.
 Interference or Superposition
Interference Is the combination of waves to give a larger
or smaller wave. As seen in the image over
← here.

S1

S2

Image showing two sets of continuous

circular waves across a ripple tank. If we look The image above shows how the pattern of
at the image we can see where the how interference or superposition is formed.
constructive interference occurs and where All points across AB are equidistance from
the destructive interference happens. At the dippers S1 and S2 which are vibrating in
points where a crest from S1 & S2 arrive at phase. This creates crests or troughs from S1
the same time a bigger crest is formed and to arrive at the same time as the crest of
the waves are in phase. At points where a trough from S2. Along the line AB
crest and a trough arrive together, they reinforcement occurs by superposition and a
cancel out each other (provided they have wave of double amplitude is formed. The
the same amplitude) and they are said to be waves along the line CD are half of a
out of phase where the water looks wavelength nearer to S1 than S2 therefore a
undisturbed. path difference of half a wavelength. This
means that the crests or troughs from S1
arrive simultaneously with troughs or crests
from S2 and the waves cancel.

Along the line EF the difference of distances

from S1 and S2 to any point along the line is
one wavelength therefore creating
superposition which makes EF a line of
The above image shows light waves falling reinforcement.
on a double slit gap creating constructive
destructive light waves on a screen. Note: if the frequency of the dippers is
increased the wavelength decreases and are
closer together. Increasing the separation
distance between the dippers also decreases
the wavelength.