Investigation #5 – Water Waves – Refraction
1. Wave Refraction – Is the bending of a wave front when it passes from
one medium to another. Two conditions will be used in explaining
refraction of water waves.
a) The boundary between the media is parallel to the incident waves
produced. Since the waves travel from deep water to shallow
water straight on no bending occurs. The wavelength is less in
the shallow water than in deep water. Since the frequency
remains the same in both regions and the wavelength is less,
then the velocity must be less in the shallow region since v = f·λ.
Boundary between water levels
Deep
Shallow
Therefore the following generalization occurs
v 1 λ1

v 2 λ2
Examples
1. The speed and the wavelength of water waves in deep water are
15.0cm/s and 2.2cm, respectively. If the velocity in shallow water is
10.0cm/s, what is the wavelength?
Solution
v1 = 15.0cm/s
v2 = 10.0cm/s
λ1 = 2.2 cm
λ2 = ?
v 1 λ1

v 2 λ2
v1λ2 = v2λ1
15.0cm/s λ2 = (10.0cm/s)(2.2cm)
λ2 = 22.0cm2/s ÷ 15.0cm/s
λ2 = 1.47cm = 1.5cm
2. Waves travel 0.75 times as fast in shallow water as they do in deep
water. What will be the wavelength of the waves in deep water, if
their wavelength is 2.0cm in shallow water?
Solution
v1 = v1
v2 = 0.75v1
λ1 = ?
λ2 = 2.0cm
v 1 λ1

v 2 λ2
v1λ2 = v2λ1
λ1 = v1λ2 ÷ v2
λ1 = v12.0cm ÷ 0.75v1
λ1 = 2.66cm = 2.7cm
b) The boundary between the media is not parallel to the incident
waves produced. Since the water wave is travelling at an angle to
the shallow water the wave will change direction when it reaches
this change of depth. This is called refraction.
Boundary between water levels
Deep
Shallow
In general, when a wave travels at an angle into a medium in
which its velocity decreases, the refracted wave ray is bent
towards the normal and if the wave velocity increases, the
refracted wave is bent away from the normal.
Investigation #6 – Water Waves – Diffraction
2. Wave Diffraction – Is the bending of waves when they pass through
small openings or edges. How much they are diffracted depends
mainly on their wavelength. Shorter wavelengths are diffracted slightly
and longer wavelengths are diffracted a greater extent as shown in the
diagrams below.
Greater
Bend
Less
Bend
As the size of the opening decreases, the amount of diffraction
increases as shown in the diagrams below.
Less
Bend
Greater
Bend
3. Interference of Waves – Occurs when two or more waves act
simultaneously on the same particles of the medium. The diagram
below shows the effect of constructive and destructive interference on
the waves.
Solid rays – Constructive
Dashed rays - Destructive