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

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/TT = 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 = fλ You 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 -7 m and a frequency of 5x10 14 Hz. What is the speed of purple light? Some example wave equation questions 0.2m 0.5m 0.6m/s 3x10 8 m/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 displacement cm

Displacement/time graph This looks at the movement of one point of the wave over a period of time 1 Time s 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 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 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 displacement cm

Displacement/distance graph This is a “snapshot” of the wave at a particular moment 1 Distance cm displacement cm WAVELENGTH

Displacement/distance graph This is a “snapshot” of the wave at a particular moment 1 Distance cm displacement cm WAVELENGTH

Displacement/distance graph This is a “snapshot” of the wave at a particular moment 1 Distance cm displacement cm WAVELENGTH IMPORTANT NOTE: This wave could also be either transverse or longitudnal

Electromagnetic spectrum

James Clerk Maxwell

Visible light

λ ≈ 700 nmλ ≈ 420 nm

Ultraviolet waves λ ≈ nm

Ultraviolet waves λ ≈ nmλ ≈ m

X-rays λ ≈ nm λ ≈ m

X-rays λ ≈ nm λ ≈ m λ ≈ m

Gamma rays λ ≈ nm λ ≈ m λ ≈ m

Gamma rays λ ≈ nm λ ≈ m λ ≈ m λ ≈ m

Infrared waves λ ≈ nm λ ≈ m λ ≈ m λ ≈ m

Infrared waves λ ≈ nm λ ≈ m λ ≈ m λ ≈ m λ ≈ m

Microwaves λ ≈ nm λ ≈ m λ ≈ m λ ≈ m λ ≈ m

Microwaves λ ≈ nm λ ≈ m λ ≈ m λ ≈ m λ ≈ m λ ≈ m

Radio waves λ ≈ nm λ ≈ m λ ≈ m λ ≈ m λ ≈ m λ ≈ m

Radio waves λ ≈ nm λ ≈ m λ ≈ m λ ≈ m λ ≈ m λ ≈ m λ ≈ m

Electromagnetic spectrum λ ≈ nm λ ≈ m λ ≈ m λ ≈ m λ ≈ m λ ≈ m λ ≈ m

What do they all have in common? λ ≈ nm λ ≈ m λ ≈ m λ ≈ m λ ≈ m λ ≈ m λ ≈ m

What do they all have in common? They can travel in a vacuum They travel at 3 x 10 8 m.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

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

Measuring the speed of sound Can you quietly and sensibly follow Mr Porter?

Measuring the speed of sound Distance = 140m Three Times = Average time = Speed = Distance/Average time = m/s

4.2 Measuring the speed of sound Measuring the speed of sound using AudacityMeasuring 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