Waves - WordPress.com2. Water waves of frequency 4Hz and wavelength 50cm travel towards a ship. Calculate the speed they travel at. 3. If the speed of sound in air is 340ms-1, calculate

Waves

Pupil Notes

Name: _________

Wallace Hall Academy Physics Department

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Learning intentions for this unit ✓ ? ✘

Be able to state that waves transfer energy.

Be able to describe the difference between longitudinal and transverse waves

and give examples of each.

Be able to perform calculations using the d=vt formula for waves.

Be able to calculate frequency, period, wavelength or amplitude of a wave

from a trace of the wave.

Be able to perform calculations using the f=n/t formula.

Be able to perform calculations using the v=fλ formula.

Be able to perform calculations using the T=1/f formula.

Be able to describe what diffraction is.

Be able to state the parts of the EM spectrum (in order) and a source, detector

and application of each.

Be able to state that the energy of EM radiation increases as frequency

increases.

Be able to state that all types of EM radiation travel at the speed of light which

is 3×108ms–1.

Be able to draw labelled diagrams demonstrating the law of reflection.

Be able to draw labelled diagrams demonstrating the law of refraction.

Be able to explain refraction in terms of wave speed.

Be able to describe how eye defects can be corrected.

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WAVE PROPERTIES

In the box below make a list of all of the different types of waves that you know about.

All waves transfer energy. Different types of waves have things in common and things that are

different but the one thing that all waves have in common is that they transfer energy. Waves can be

grouped into one of two types, longitudinal or transverse.

Longitudinal waves

In a longitudinal wave the vibration of particles is in the same direction as the direction the

wave is travelling in.

Sound is the most common example of a longitudinal wave.

Transverse waves

In a transverse wave the particles vibrate at right angles to the direction the wave is

travelling in.

Light and all other electromagnetic waves (such as radio waves) are transverse waves.

Types of waves

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Wave Speed

The speed of an object or a wave can be worked out from the following equation:

d =

v =

t =

Example

A water wave travels a distance of 20 m in 4 s. Calculate the speed of the wave.

Practice Problems

1. A water wave travels at a speed of 3 ms-1 for a distance of 15 m. Calculate how long this will

take.

2. A Mexican wave travels a distance of 120 m round a stadium in a time of 6 s. Calculate how

fast the wave was moving.

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Experiment – measuring the speed of sound

You will measure the speed of sound outside by creating a sound wave and reflecting it off the PE

department.

Aim: To measure the speed of sound

Diagram:

Method:

Results:

Distance to PE block =

Distance the sound wave travelled =

Time (s)

Average time =

Speed of sound calculation

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Conclusion:

Evaluation: (What improvements could be made to the experiment?)

Wavelength

The wavelength of a wave is simply the length of one

wave. It can be found by measuring the distance from

peak to peak, trough to trough or between

corresponding zero crossings.

Wavelength is measured in metres (m) and it has the

symbol λ (lambda).

Amplitude

The amplitude of the wave is the height of the

wave from the middle point of the wave.

The units of amplitude vary depending on the

type of wave. For instance; for water waves

the amplitude is measured in metres, for

electrical waves the amplitude is measured in

volts and for sound waves amplitude is

measured in decibels.

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Practice Problems

For the following wave traces determine:

• The number of waves shown

• The wavelength of the wave

• The amplitude of the wave

Number =

Wavelength =

Amplitude =

Number =

Wavelength =

Amplitude =

Number =

Wavelength =

Amplitude =

Number =

Wavelength =

Amplitude =

15m

6m

24m

10mm

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Frequency

Frequency is a measure of the number of waves passing a point per second. The frequency of

a wave can be worked out from the following equation:

f =

n =

t =

Example 1

A wave has a frequency of 3 Hz. Calculate how many waves will pass in 6 s?

Example 2

A wave has a frequency of 12 Hz. Calculate how long it will take for 3 waves to pass?

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Practice Problems

1. If 10 waves pass a point in 2s, what is the frequency of the waves?

2. A boy counts 24 water waves hitting a beach in 4 minutes. Calculate the frequency of the

waves?

3. A swimmer at a pool measures the frequency of waves in the water to be 3 Hz. Calculate how

long it will take for 27 waves to pass him?

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Period

The period of a wave is the time taken for one wave to pass a particular point. The period of a

wave can be worked out from the following equation:

T =

f =

1=

Example 1

A wave has a frequency of 3 Hz. Calculate its period.

Example 2

A wave has a period of 0.2 s. Calculate its frequency.

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Practice Problems

1. A wave has a frequency of 20 Hz. Calculate its period.

2. A wave has a period of 4 s. Calculate its frequency.

3. A wave has a period of 25 s. Calculate its frequency.

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The Wave Equation

There is a second way to calculate the speed of waves. Instead of using the distance, speed and

time formula we can instead use the fact that the speed of a wave is equal to the frequency of a

wave multiplied by its wavelength. This formula appears on the formula sheet and is given below:

v =

f =

=

Example

A sound wave travelling at 340ms–1 has a frequency of 256Hz. Calculate its wavelength.

Practice Problems

1. The frequency of sound waves coming from a loudspeaker is 170Hz and their wavelength is

2m. Calculate the speed they travel at.

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2. Water waves of frequency 4Hz and wavelength 50cm travel towards a ship. Calculate the

speed they travel at.

3. If the speed of sound in air is 340ms-1, calculate the wavelength of sound waves with a

frequency of 512Hz.

4. Water waves travel towards a lifeboat at a speed of 2.5ms-1 with a wavelength of 0.5m.

Calculate their frequency.

5. A water wave takes 1.5s to travel 6m. If the frequency of the wave is 2Hz, calculate the

wavelength of the wave.

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Diffraction

Diffraction is what happens when waves bend round an object. Diffraction is a property of all

waves, it is also a unique property of waves.

Diffraction of sound waves is why

sounds can be heard around a corner.

The amount of diffraction depends on wavelength. The longer the wavelength, the greater the

diffraction.

You cannot see around a corner because light waves have a much shorter wavelength than sound

waves and so are not diffracted round the corner. Radio and T.V. waves also diffract around objects.

The amount they diffract depends on their wavelength.

Radio waves have a longer wavelength than TV waves and therefore diffract more. In hilly areas it is

much easier to receive radio signals than TV signals because of this. Mobile phones use

microwaves which have an even shorter wavelength than TV signals, this is why it is very difficult to

get reception in hilly areas.

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THE ELECTROMAGNETIC SPECTRUM

Visible Light

Light is a transverse wave and like all waves it can be described as having peaks, troughs,

frequency, wavelength and amplitude. Just like all other waves it transfers energy. As well as visible

light there is also light all around us which is invisible.. We call the whole family of light waves (the

ones we can see and the ones we can’t) the Electromagnetic Spectrum and the waves

Electromagnetic Waves (EM).

The Electromagnetic Spectrum

All EM waves are transverse waves. All EM waves travel at the speed of light (300,000,000 ms–1 or

3×108 ms–1). All EM waves have different frequencies and wavelengths depending on what part of

the electromagnetic spectrum they belong to.

The seven parts of the Electromagnetic Spectrum are shown below. Create a mnemonic to

remember the order.

G Gamma ______________

X X-Rays ______________

U Ultraviolet (UV) ______________

V Visible ______________

I Infra-red (IR) ______________

M Microwaves ______________

R Radio & TV ______________

incre

asin

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ave

leng

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incre

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g fre

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Violet Red

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You will now select one of the seven sections of the electromagnetic spectrum and prepare a

presentation to be given to the rest of the class. While others are completing their presentations you

should complete the table below.

Section of

EM spectrum

Source Detector Use

Gamma

X-Rays

Ultraviolet

Visible

Infra-red

Microwaves

Radio & TV

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Frequency and Energy

Although the amplitude of an electromagnetic wave is related to the energy of the wave this is not

the whole story. In Physics we refer to the amplitude of light as its intensity.

However the energy of electromagnetic wave is not only dependent on its intensity. You are

probably aware that high frequency EM waves, such as gamma rays, are far more energetic (and

dangerous) than low frequency EM waves, such as radio waves, even though they might have the

same intensity.

This is because the energy of an electromagnetic wave does not travel as a continuous stream but

in ‘packets’ or ‘bundles’. We call these packets of energy photons. The energy of a photon is

proportional to the frequency of the light.

Waves with higher frequencies have higher photon energy (gamma).

Waves with lower frequencies have lower photon energy (radio & TV).

Practice Problems

1. If it takes light 8 minutes to travel from the Sun to the Earth, calculate how far away the Sun is

from Earth.

2. Calculate the frequency of red light which has a wavelength of 700nm.

3. Calculate the wavelength of green light which has a frequency of 5.8×1014Hz.

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LIGHT

Reflection

You will already know that light reflects from shiny surfaces. Complete the diagram below showing

the path of the ray of light as it reflects from the mirror. Label the normal, both angles and both rays

of light.

Remember the angles of incidence and reflection are always measured relative to the normal.

Reflection is also used in curved reflectors. This is how the satellite dishes on the side of houses

collect TV signals and how satellites in orbit around the Earth send and receive signals. Complete

the diagram below to show how a curved reflector works.

Curved reflectors are used to increase the strength of signals which are received by

gathering lots of rays and reflecting them towards an aerial. The bigger the curved reflector is,

the stronger the signal. They can also be used to transmit a signal in one direction towards a

receiver by gathering lots of rays and reflecting them outwards as parallel rays.

mirror

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Refraction

Refraction is when light changes speed when going from one material to another. Refraction

also usually results in light changing direction when going from one material to another.

Complete the diagram below showing the path of the ray of light as it passes through the glass

block. Label the normal, all angles and all rays of light.

Remember the angles of incidence and refraction are always measured relative to the

normal.

Complete the diagram below showing the path of the ray of light as it passes through the glass

block. Label the normal, all angles and all rays of light.

You will notice that the white light splits up into different colours. This splitting is called dispersion.

When going from air to a more dense material light refracts __________________ the normal.

When going from a more dense material to air light refracts __________________ the normal.

glass

glass

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Total internal reflection

Complete the two diagrams below showing the path of the ray of light as it passes through the glass

block. Label the normal, both angles and both rays of light.

As you can see depending on what the size of the incident angle is the light will either refract or

reflect. When the angle of incidence is small the light will refract. When the angle of incidence is big

the light will reflect.

There is an incident angle in between refraction and reflection occurring where the ray refracts at

900 to the normal. This incident angle is called the critical angle.

At all incident angles below the critical angle light is _________________________________

At all incident angles above the critical angle light is _________________________________

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When light is reflected within glass it is a special type of reflection called total internal reflection.

Total internal reflection is how light travels down an optical fibre.

Lenses

There are two basic types of lenses which are shown below. Complete both diagrams showing the

path of the parallel rays of light through them and name both lenses. You should also label the focal

length and focal point on the convex lens.

Type of lens: _______________

Type of lens: _______________

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The eye

Lenses have a variety of uses in everyday life.

You will have a small convex lens on the

camera on your smartphone and they are used

in telescope and binoculars but the most

common use is in spectacles to correct eye

defects.

Your eye contains a variety of different parts as

shown opposite. The two important parts for

this part of the course are the lens and the

retina.

The convex lens in your eye focusses rays of light onto the retina. Complete the diagram below to

show this.

People who are short sighted or long sighted wear glasses to correct these eye defects.

Short sighted – cannot see far away objects clearly and rays focus short of the retina.

Corrected with a concave lens.

Long sighted – cannot see nearby objects clearly and rays focus long of the retina. Corrected

with a convex lens.

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Prefixes

Physics deals with the very big (space) and with the very small (atoms) so it is often useful to use

prefixes when describing values involved in equations.

Subscript What does it mean? What do I do?

Giga - G 1 000 000 000 times bigger x 109

Mega - M 1 000 000 times bigger x 106

kilo - k 1 000 times bigger x 103

milli - m 1 000 times smaller x 10-3

micro - 1 000 000 times smaller x 10-6

nano - n 1 000 000 000 times smaller x 10-9

Example

Susie completes a 3.4 km journey in her car. How many m is this?

Practice problems

1. John measures a piece of wood to be 3 mm thick. Calculate how many m this is.

2. Jack measures a voltage to be 6.2 MV. Calculate how many V this is.

3. The wavelength of red light is 633 nm. Calculate how many m this is.

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Scientific notation

As well as using prefixes it may also be useful to use scientific notation to describe very big or very

small numbers. Numbers with a positive power of 10 are very large and numbers with a negative

power of 10 are very small.

Standard form Scientific notation

400 000 4 x 105

5600 5.6 x 103

0.000 000 007 7 x 10-9

0.000 038 3.8 x 10-5

Example

The speed of light is 300 000 000 ms-1. Convert this into scientific notation.

Practice problems

1. Convert 260 000 into scientific notation.

2. Convert 7.4 x 103 into standard form.

3. Convert 3.64 x 10-7 into standard form.