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5 July, 2017
The Wave Equation.
Objectives
Be able to define wave speed, frequency and
wavelength and use the wave equation.
HSW: AF5: Process data using multi-step calculations to identify complex
relationships between variables.
Used before in:
Will use again in:
PLTS: Independent enquirers: support conclusions, using reasoned arguments and evidence.
Used before in:
Will use again in:
Keywords
Wavelength, lamda, amplitude, frequency, Hertz, kilohertz,
megahertz, speed, metres, kilometres.
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Outcomes
All students should be able to:
• Define wave-speed, wavelength and
frequency and recall the units.
Most students should be able to:
• Be able to use the wave equation.
Some students should be able to:
• Be able to recall the wave equation and
rearrange it for wave-speed, wavelength
and frequency and recall the symbols for
each.
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wavelength
Lamda
amplitude
frequency
Hertz
kilohertz
megahertz
speed
kilometres
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Quantity
Symbol
Unit
Speed
f
m
Frequency
λ
m/s
Wavelength
v
Hz
Write a definition for speed, frequency and wavelength.
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Demo time
• Your teacher will demonstrate to you
how wave-speed, frequency and
wavelength are related.
• See if you can come up with the
relationship yourself.
• What happens to the wavelength when
the frequency stays constant but the
speed increases? Does it go up or
down?
• What happens when the frequency
increases but the speed stays the
same?
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How is wave speed calculated?
These waves are travelling across
the surface of a pond. The length
of each wave is 0.25 m.
Two waves pass the duck each
second, so the frequency is 2 Hz.
This means that the waves travel
0.5 m each second, so the
speed of the waves is 0.5 m/s.
From this example, the connection between speed, frequency
and wavelength is:
speed = frequency x wavelength
0.5 m/s =
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2 Hz
x
0.25 m
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What is the formula for wave speed?
For any set of waves, the wave speed (v) can be calculated
from the frequency (f) and wavelength () using this formula:
wave speed = frequency x wavelength
v = f x 
What are the units of speed, frequency and wavelength?
 Wave speed is measured in metres per second (m/s).
 Frequency is measured in hertz (Hz).
 Wavelength is measured in metres (m).
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Can I use a formula triangle?
A formula triangle helps you to rearrange a formula.
The formula triangle for wave speed (v), frequency (f)
and wavelength () is shown below.
Cover the quantity that you are trying to work out, which
gives the rearranged formula needed for the calculation.
So to find frequency (f),
cover up f…


…which gives
the formula…
f =
v

x
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Calculating wave speed – example
These waves are rippling
across a pond.
The frequency of the
waves is 0.2 Hz and the
length of each wave is
estimated at 0.15 m.
What is the wave speed?
wave speed = frequency x wavelength
=
0.2 Hz
x
0.15 m
= 0.03 m/s
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Units
Take care
• Kilo means: One thousand times: 1000 x
• Mega means: One Million times: 1000 000 x
• km = kilometres = 1000 m
• MHz = MegaHertz = 1000 000 Hz
• GHz = GigaHertz = 1000 000 000 Hz
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TASK – Wave equation worksheet
• Work with the person next to you and
see how many of the questions you can
do using the wave equation.
• They will give you great practise at
using it.
• Your teacher will set you a time limit of
up to 30 mins
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Outcomes – How have you done? Look below and rate
yourself:
All students should be able to:
• Define wave-speed, wavelength and
frequency and recall the units.
Most students should be able to:
• Be able to use the wave equation.
Some students should be able to:
• Be able to recall the wave equation and
rearrange it for wave-speed, wavelength
and frequency and recall the symbols for
each.
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Wave speed problems
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