The Wave Equation

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The Wave Equation.

22 April 2023

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:

KeywordsWavelength, lamda, amplitude, frequency, Hertz, kilohertz,

megahertz, speed, metres, kilometres.


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.


wavelength Lamda amplitude

frequency Hertz kilohertz

megahertz speed kilometres


Speed

Frequency

Wavelength

Quantity Symbol Unit

f

λ

v

m/s

Hz

m

v

m/sλ

f m

Hz

Write a definition for speed, frequency and wavelength.


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?


These waves are travelling across the surface of a pond. The length of each wave is 0.25 m.

From this example, the connection between speed, frequency and wavelength is:

How is wave speed calculated?

speed = frequency x wavelength

0.5 m/s = 2 Hz x 0.25 m

This means that the waves travel 0.5 m each second, so the speed of the waves is 0.5 m/s.

Two waves pass the duck each second, so the frequency is 2 Hz.


Wave speed is measured in metres per second (m/s).

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:

What are the units of speed, frequency and wavelength?

Frequency is measured in hertz (Hz).

Wavelength is measured in metres (m).

wave speed = frequency x wavelength

v = f x


x

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…

Can I use a formula triangle?

f =v


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?

Calculating wave speed – example

wave speed = frequency x wavelength

= 0.2 Hz x 0.15 m

= 0.03 m/s


Units

• 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

Take care


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


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.


Wave speed problems

Documents

The Wave Equation