4.2 Travelling waves

What is a (travelling) wave?

Waves

Waves can transfer energy and information without a net motion of the medium through which they travel.

They involve vibrations (oscillations) of some sort.

Wave fronts

Wave fronts highlight the part of a wave that is moving together (in phase).

= wavefront

Ripples formed by a stone falling in water

Rays

Rays highlight the direction of energy transfer.

Transverse waves

The oscillations are perpendicular to the direction of energy transfer.

Direction of energy transfer

oscillation

Transverse waves

Transverse waves

Transverse waves

Transverse waves

peak

trough

Transverse waves

• Water ripples

• Light

• On a rope/slinky

• Earthquake (s)

Longitudinal waves

The oscillations are parallel to the direction of energy transfer.

Direction of energy transfer

oscillation

Longitudinal waves

compression

rarefraction

Longitudinal waves

• Sound

• Slinky

• Earthquake (p)

Other waves - water

A reminder – wave measurements

Displacement - x

This measures the change that has taken place as a result of a wave passing a particular point.

Zero displacement refers to the average position.

= displacement

Amplitude - A

The maximum displacement from the mean position.

amplitude

Period - T

The time taken (in seconds) for one complete oscillation. It is also the time taken for a complete wave to pass a given point.

One complete wave

Frequency - f

The number of oscillations in one second. Measured in Hertz.

50 Hz = 50 vibrations/waves/oscillations in one second.

Wavelength - λ

The shortest distance between points that are in phase (points moving together or “in step”).

wavelength

Wave speed - v

The speed at which the wave fronts pass a stationary observer.

330 m.s-1

Period and frequency

Period and frequency are reciprocals of each other

f = 1/T T = 1/f

The Wave Equation

The time taken for one complete oscillation is the period T. In this time, the wave will have moved one wavelength λ.

The speed of the wave therefore is distance/time

v = λ/T = fλYou need to be able to derive this!

1) A water wave has a frequency of 2Hz and a wavelength of 0.3m. How fast is it moving?

2) A water wave travels through a pond with a speed of 1m/s and a frequency of 5Hz. What is the wavelength of the waves?

3) The speed of sound is 330m/s (in air). When Dave hears this sound his ear vibrates 660 times a second. What was the wavelength of the sound?

4) Purple light has a wavelength of around 6x10-7m and a frequency of 5x1014Hz. What is the speed of purple light?

Some example wave equation questions

0.2m

0.5m

0.6m/s

3x108m/s

Let’s try some questions!

4.2 Wave equation questions

Representing waves

There are two ways we can represent a wave in a graph;

Displacement/time graph

This looks at the movement of one point of the wave over a period of time

1

Time s

-1

-2

0.1 0.2 0.3 0.4

displacement

cm

Displacement/time graph

This looks at the movement of one point of the wave over a period of time

1

Time s

-1

-2

0.1 0.2 0.3 0.4

displacement

cm

PERIOD

Displacement/time graph

This looks at the movement of one point of the wave over a period of time

1

Time s

-1

-2

0.1 0.2 0.3 0.4

displacement

cm

PERIOD

Displacement/time graph

This looks at the movement of one point of the wave over a period of time

1

Time s

-1

-2

0.1 0.2 0.3 0.4

displacement

cm

PERIOD

IMPORTANT NOTE: This wave could be either transverse or longitudnal

Displacement/distance graph

This is a “snapshot” of the wave at a particular moment

1

Distance cm

-1

-2

0.4 0.8 1.2 1.6

displacement

cm

Displacement/distance graph

This is a “snapshot” of the wave at a particular moment

1

Distance cm

-1

-2

0.4 0.8 1.2 1.6

displacement

cm

WAVELENGTH

Displacement/distance graph

This is a “snapshot” of the wave at a particular moment

1

Distance cm

-1

-2

0.4 0.8 1.2 1.6

displacement

cm

WAVELENGTH

Displacement/distance graph

This is a “snapshot” of the wave at a particular moment

1

Distance cm

-1

-2

0.4 0.8 1.2 1.6

displacement

cm

WAVELENGTH

IMPORTANT NOTE: This wave could also be either transverse or longitudnal

Electromagnetic spectrum

James Clerk Maxwell

Visible light

Visible light

λ ≈ 700 nm λ ≈ 420 nm

Ultraviolet waves

λ ≈ 700 - 420 nm

Ultraviolet waves

λ ≈ 700 - 420 nm λ ≈ 10-7 - 10-8 m

X-rays

λ ≈ 700 - 420 nm

λ ≈ 10-7 - 10-8 m

X-rays

λ ≈ 700 - 420 nm

λ ≈ 10-7 - 10-8 m

λ ≈ 10-9 - 10-11 m

Gamma rays

λ ≈ 700 - 420 nm

λ ≈ 10-7 - 10-8 m

λ ≈ 10-9 - 10-11 m

Gamma rays

λ ≈ 700 - 420 nm

λ ≈ 10-7 - 10-8 m

λ ≈ 10-9 - 10-11 mλ ≈ 10-12 - 10-15 m

Infrared waves

λ ≈ 700 - 420 nm

λ ≈ 10-7 - 10-8 m

λ ≈ 10-9 - 10-11 m

λ ≈ 10-12 - 10-15 m

Infrared waves

λ ≈ 700 - 420 nm

λ ≈ 10-7 - 10-8 m

λ ≈ 10-9 - 10-11 m

λ ≈ 10-12 - 10-15 m

λ ≈ 10-4 - 10-6 m

Microwaves

λ ≈ 700 - 420 nm

λ ≈ 10-7 - 10-8 m

λ ≈ 10-9 - 10-11 m

λ ≈ 10-12 - 10-15 m

λ ≈ 10-4 - 10-6 m

Microwaves

λ ≈ 700 - 420 nm

λ ≈ 10-7 - 10-8 m

λ ≈ 10-9 - 10-11 m

λ ≈ 10-12 - 10-15 m

λ ≈ 10-4 - 10-6 m

λ ≈ 10-2 - 10-3 m

Radio waves

λ ≈ 700 - 420 nm

λ ≈ 10-7 - 10-8 m

λ ≈ 10-9 - 10-11 m

λ ≈ 10-12 - 10-15 m

λ ≈ 10-4 - 10-6 m

λ ≈ 10-2 - 10-3 m

Radio waves

λ ≈ 700 - 420 nm

λ ≈ 10-7 - 10-8 m

λ ≈ 10-9 - 10-11 m

λ ≈ 10-12 - 10-15 m

λ ≈ 10-4 - 10-6 m

λ ≈ 10-2 - 10-3 m

λ ≈ 10-1 - 103 m

Electromagnetic spectrum

λ ≈ 700 - 420 nm

λ ≈ 10-7 - 10-8 m

λ ≈ 10-9 - 10-11 m

λ ≈ 10-12 - 10-15 m

λ ≈ 10-4 - 10-6 m

λ ≈ 10-2 - 10-3 m

λ ≈ 10-1 - 103 m

What do they all have in common?

λ ≈ 700 - 420 nm

λ ≈ 10-7 - 10-8 m

λ ≈ 10-9 - 10-11 m

λ ≈ 10-12 - 10-15 m

λ ≈ 10-4 - 10-6 m

λ ≈ 10-2 - 10-3 m

λ ≈ 10-1 - 103 m

What do they all have in common?

• They can travel in a vacuum• They travel at 3 x 108m.s-1 in a vacuum

(the speed of light)• They are transverse• They are electromagnetic waves (electric

and magnetic fields at right angles to each oscillating perpendicularly to the direction of energy transfer)

What do you need to know?

• Order of the waves

• Approximate wavelength

• Properties (all have the same speed in a vacuum, transverse, electromagnetic waves)

• The Electromagnetic Spectrum

Sound

Sound travels as Longitudinal waves

The oscillations are parallel to the direction of energy transfer.

Direction of energy transfer

oscillation

Longitudinal waves

compression

rarefaction

Amplitude = volume

Pitch = frequency

Range of hearing

Range of hearing

Humans can hear up to a frequency of around 20 000 Hz (20 kHz)

Measuring the speed of sound

Can you quietly and sensibly follow Mr

Porter?

Measuring the speed of sound

• Distance = 140 m

• Three Times =

• Average time =

• Speed = Distance/Average time = m/s

4.2 Measuring the speed of sound

• Measuring the speed of sound using Audacity

String telephones

Sound in solids

• Speed ≈ 6000 m/s

Sound in liquids

• Speed ≈ 1500 m/s

Sound in gases (air)

• Speed ≈ 330 m/s

Sound in a vacuum?

echo

• An echo is simply the reflection of a sound