P1c(i) A Spectrum of Waves

You will learn about:The features of transverse waves

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Transverse Waveswww.PhysicsGCSE.co.uk A spring moving up and down

represents a transverse wave. Just like a Mexican wave or when a pebble is dropped into a puddle of water. A rippling effect occurs.

The x-axis shows time.If the wave is at x=0 then this shows the rest position.

The maximum displacement from the x-axis shows the amplitude of the wave. It is measured in metres.Remember: this is above the x-axis as well as below the x-axis. A transverse wave is symmetrical.

This is a trough: maximum displacement below the rest position

This is a crest: maximum displacement from the rest position

The y-axis shows how much energy there is.

It shows how much the wave vibrates from the rest position.

This represents one wavelength. It is measured in metres.

Remember: A wavelength can also be the distance from crest to crest OR trough to trough.

The frequency of a wave is measured by the number of waves per second.The unit of frequency is the Hertz (Hz).

6Hz because there are six waves in one second.This is the higher frequency wave.

3Hz because there are three waves in one second.This is the lower frequency wave.

REMEMBER: The distance between the surfer, at the trough of the wave, and the crest of this wave is 20 metres. This means that that the amplitude is half this – 10 metres.

Energy in a Transverse Wavewww.PhysicsGCSE.co.uk

A Transverse wave travels in the direction at RIGHT ANGLES to the wave vibration.

The wave overall is moving this way over a period of time… so the energy of the wave is moving in the same direction too.Transverse waves are slow because they do not travel in straight lines… they move up and down along the way.

Contextualisation:

So, the wave moves up and then down and then up and so on. This up and down motion is 90 degrees to the direction of right.

Here a pebble has been dropped into a pond. You can see the ripples made.The centre of the ripples illustrates our 0,0 or origin point on our graph.

You can see two more features in the ripples.The ripples have high points and they have low points.The high points are represented as crests on the graph.

The low points are represented as troughs on the graph.

One wavelength would be the distance between crests OR troughs.The frequency would be the number of waves in one second. If this image was over a one second interval then you can count the number of peaks (white parts) as seven. Thus frequency is 7 Hz.

Calculating wave speedwww.PhysicsGCSE.co.uk

REMEMBER:Use the triangle rule to re-arrange this equation.

A surfer rides a series of 20 waves that are each separated by a distance of 2.5 metres in 10 seconds.Calculate the wave speed.

First we need to work out the frequency:This is the number of waves in each second.We are told that there are 20 waves in 10 seconds. So for each second the surfer passes 2 waves. So frequency is 2 Hz.For wave speed use equation: 5 m/s

REMEMBER: ALL Electromagnetic waves have the same speed in a vacuum: 300,000,000 m/s

Questions

1. If the wavelength of a wave decreased what would happen to its frequency?

2. The speed of sound is about 330 m/s. During a thunderstorm why do we see lightning before we hear the thunder?

3. Radio waves and Gamma waves have very different frequencies. What can you say about their speeds?

4. A dolphin produces a sound with a frequency of 120,000 Hz. If the wavelength is 1.25 cm calculate the speed of sound in water.

5. A Radio wave is broadcasted at 200 kHz. Calculate the wavelength of this broadcast.

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Questions1. If the wavelength of a wave decreased what would happen to its frequency?

Frequency would increase (as there is a smaller distance between each wave)2. The speed of sound is about 330 m/s. During a thunderstorm why do we see

lightning before we hear the thunder? Lightning travels very much faster than sound. In fact sound travels in air ~330 m/s whereas light travels ~300,000,000 m/s.

3. Radio waves and Gamma waves have very different frequencies. What can you say about their speeds? They have the same speed: 300,000,000 m/s.

4. A dolphin produces a sound with a frequency of 120,000 Hz. If the wavelength is 1.25 cm calculate the speed of sound in water. Wave speed = frequency x wavelength. Notice that the unit for wavelength is not in metres so this needs to be converted first. 1.25 cm = 0.0125 m. So wave speed = 120,000 Hz x 0.0125 m = 1,500 m/s

5. A Radio wave is broadcasted at 200 kHz. Calculate the wavelength of this broadcast. All Electromagnetic waves have the same speed. So

Radio waves travel at 300,000,000 m/s. We also need to convert 200kHz into Hz. k means kilo or 1,000. So 200 kHz = 200,000 Hz. We need to re-arrange the wave speed equation to give us wavelength. So wavelength = = = 1,500 metres

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