Basics of Geophysical Fluid Dynamics

3.6 Exercise 2: Wave Interference 25

3.5.10 Superposition of Waves

The superposition of two or more waves of different period and/or wavelength can

lead to various interference patterns such as a standing wave, being a wave of vir￾tually zero phase speed. Interfering wave patterns travel with a certain speed, called

group speed that can be different to the phase speeds of the contributing individual

waves. Interference of storm-generated waves in the ocean can result in waves of

gigantic wave heights (wave height is twice the wave amplitude) of >20 m, known

as freak waves.

3.6 Exercise 2: Wave Interference

3.6.1 Aim

The aim of this exercise is to explore interferences that result from the superpo￾sition of two linear waves. To this end, SciLab will be used to calculate possible

interferences pattern and to produce animations thereof.

3.6.2 Task Description

Consider the interference of two waves of the same amplitude of Ao = 1 m. The

resultant wave can be described by:

A(x, t) = Ao



sin 

2π

 x

λ1

− t

T1

 + sin 

2π

 x

λ2

− t

T2



Using SciLab, the reader is asked to produce animations considering the follow￾ing interference scenarios. In all scenarios, wave 1 has a period of T1 = 60 s and

a wavelength of λ1 = 100 m. Choose period and wavelength of wave 2 from the

following list:

Scenario 1: wavelength = 100 m; wave period = 50 s

Scenario 2: wavelength = 90 m; wave period = 60 s

Scenario 3: wavelength = 90 m; wave period = 50 s

Scenario 4: wavelength = 100 m; wave period = −60 s

Scenario 5: wavelength = 50 m; wave period = −30 s

Scenario 6: wavelength = 95 m; wave period = −30 s.

These scenarios describe a variety of interference patterns. Scenario 4, for

instance, leads to a standing wave, being the result of two identical waves travelling

in opposite directions. This is achieved by prescribing a negative value of the wave

period for wave 2. Is this surprising how many different interference patterns can be

created by superposition of just two waves. The reader is encouraged to experiment

with other scenarios!