4.4.1

• Wave pulse: a wave pulse is a short wave with no repeated oscillations

• Progressive wave: a wave that moves through a medium transferring energy as it travels

In longitudinal waves,particles will 'bump' into each other, so one particle will set the other in motion, which in turn moves the next, and so on.

4.1.2 – State that waves transfer energy

Transverse waves work similarly, except that the particles up and down motion causes the next particle to begin moving, and so the energy is transferred.

Waves transfer energy by moving it from one particle to the next,not by moving the particles along with the wave. there is no net motion of the medium through which the wave travels.

4.4.3 – Transverse and Longitudinal Waves- They are mechanical waves which propagate through materials (solids, liquids and gases).

Longitudinal – The displacement of the particles is parallel to the wave.

Example – Sound waves in air.

Transverse – The dispcament of the particles is perpendicular to the wave (the particles travel at 90º to the wave)

Examples – Ripples on a pond or waves on a string.Transverse waves cannot propagate in gases.

4.4.4 WAVE FRONT VS. WAVE RAY

In a circular wave (dipping your finger in a pond) you see a circular ripple moving in every direction from the point where you put your finger in. The circular ripple itself is the wave front as it is a continuous line that shows the distance reached by the wave at a certain time.

While the wave ray is the direction that a point is moving away from a point. Wave ray are perpendicular to the wave front.

In a straight wave the plane of the wave is the wave front while the direction the wave is moving is the wave ray

4.4.5describe the terms ‘crest, trough, compression and

rarefaction’

Crest

trough

Compression

rarefaction

In a longitudinal wave it is where the density is the highest.

In a longitudinal wave it is where the density is the lowest.

http://www.youtube.com/watch?v=Rbuhdo0AZDU&feature=related

4.4.6 Displacement, Amplitude, Period, Frequency, Wavelength and Wave speed

Displacement• In the context of waves, this refers to the movement of particles above

and below the mean position. • Over a period of time, the average position of a particle in the medium will

be the same as if there were no wave traveling through it. • Displacement is not only a measure of distance from an initial position to

a final position, it is also a vector, which means it has direction.• It is measured in metres

Amplitude• The difference between the maximum displacement and the mean

position, i.e. the height of the wave. • Amplitude means a measure of the amount of energy in a wave• Measured in meters

Period (T)• Amount of time for one complete cycle (i.e. from one peak to the next, or

one compression to the next)• It is inversely proportional to Frequency (T = 1/f)

Wavelength• The distance covered in by complete wave cycle (i.e. from one crest to the

next)• Wavelength = wave speed/frequency

• Represented by .

Wave Speed• The speed at which a given point on the wave is traveling through the

medium (i.e. how far a particular crest travels in a second)• The velocity of propagation of a wave depends on the properties of the

medium through which it moves ( e.g. faster in Air than in water etc).• The wave speed, the frequency, and the wavelength are related by the

formula ---------- x = f Where: = WavelengthF = FrequencyX = wave speed

4.4.7

4.4.8 derive and apply the relationship between wave speed, wavelength, and frequency.

v = λf

v = d/t unit: ms-1

f = cycles per second unit: s-1 (Hz) λ = distance per cycle unit: mTo get the correct unit (ms-1) you must multiply f and λ.v = λfv = m x s-1

V = ms-1

4.4.8 derive and apply the relationship between wave speed, wavelength, and frequency.

v = λf v = 2.0m x 10Hzv = 20 ms-1

A wave has a wavelength of 2.0m and a frequency of 10Hz. Find the velocity of the wave.

4.4.9 Wave speed and Wavelengths • Electromagnetic waves are magnetic fields and electric fields oscillating at right angles to each other•All electromagnetic waves travel at the same speed in free space

4.5.1 Describe the reflection and transmission of waves at a boundary between two media: This should include the sketching of incident, reflected, and transmitted waves.

•Media- the medium of the wave, what the wave is traveling in.•Incident wave- the original wave that hits the boundary•Transmitted wave- the refracted wave, the wave that passes into the new medium

At every boundary some of the energy is reflected (bounces off the new medium) and some is transmitted (passes into the new medium), how that happens depends on the nature of the boundary.

http://www.surendranath.org/Applets/Waves/TwaveRefTran/TwaveRefTranApplet.html animation of waves reflected from different boundaries.

•How is a wave reflected from an open end (lower index of refraction)?•How is a wave reflected from a closed end (higher index of refraction)?•How is a wave transmitted at different boundaries? Compare the strings to indices of refraction.

Diagram of the reflection and transmission of a light wave at the boundary between air and another medium

Snell’s Law

4.5.2State and apply Snell’s law

Pre-requisite- Refraction When a wave travelling in one medium crosses a boundary into a medium where its velocity is different, it may move in a different direction than the incident wave.

Ѳ1=incident angle

Ѳ2=angle of refraction

Snells Law

Describes relationship between the different angles of light and/or velocities as it passes from one medium to another.

States that the ratio of the sine of the angles of incidence and refraction is equivalent to the ratio of velocities in the two mediums.

Application

` Note- n1 and n2 represent the refractive index of the mediums

Example- An earthquake wave passes across a boundary of rock where its velocity increases from 6.5km/s to 8.5km/s. If it strikes the boundary at 30⁰, what is the angle of refraction?

Sin 30 ⁰/sin Ѳ2=v1/v2=(sin30⁰)/ (6.5/8.5)=41 ⁰

Useful sites

http://interactagram.com/physics/optics/refraction/

http://en.wikipedia.org/wiki/Snell's_law

4.5.3 Explain and discuss qualitatively the diffraction of waves at apertures and obstacles

• Diffraction is the bending of a wave around objects or the spreading after passing through a gap.

• Huygens Principle states: The direction of travel is perpendicular to the wavefront.Each individual point is the centre of its own circular wavefront.

• Diffraction processes are most noticeable when the obstruction or gap ( aperture ) is about the same size as the wavelength of the impinging wave

• In diffraction the wave remains in the same medium and so its speed, frequency and wavelength remain the same. The only thing that changes is the direction of the wave as it passes around obstacles or through gaps.

The smaller the gab the larger the Diffraction will be.

The wider the gab the smaller the diffraction will be.

• Lower frequency waves will have a higher diffraction than a high frequency wave.

• As a general rule, the amount of diffraction will depend on the ratio of the wavelength (lamda) of the sound for example to the width (w) of the aperture or obstacle.

• For small wavelengths, lamda is small compared to width which means that the diffraction will be small.

• For long wavelengths, lamda is large compared to width which means that larger diffraction will occur.

4.5.4Examples of diffraction

Waves spread as they travel, and when they encounter an obstacle they somewhat bend around it. Amount of diffraction depends on the wavelength and the size of the obsticle.

4.5 Wave Properties

4.5.5 - State the principle of superposition and explain what is meant by constructive

interference and destructive interference in terms of path difference and phase difference.

• Principle of Superposition– When two waves overlap the resultant displacement is the algebraic sum of

their separate amplitudes.

• Constructive Interference– When the crests or troughs of

two waves (opposing each other in phase) overlap, the superposition wave reaches a maximum height. The maximum height is the sum of their amplitudes.

• Destructive Interference– When the crest of one wave overlaps

with the trough of another wave opposing, the waves cancel each other out.

4.5.6 – Conditions for constructive and Destructive interference

Constructive • In phase when crest meets crest. • Anti nodes at maximum constructive

interference (red)

• Phase difference comes when two waves of the same frequency, travel different distances therefore not in phase when waves meet

• Path difference = nλ

Destructive • In phase, when crest meets trough.• Nodes – no displacement of water (blue)

• Only in phase if difference in distance travelled is an integral number of waves

• Miniuim difference = (n+ (1/2))λ

Two source interference pattern

4.5.7 Apply the principle of superpositionto determine the resultant of two

waves.Superposition is when two waves interfere. The resultant wave of this interference has an amplitude equal to the addition of the amplitudes of the interfering waves.

So when the amplitudes of two interfering waves are equal but opposite in sign they will cancel out because amplitude will = X + (-X)= 0

Note• if the wave is in the downward direction (bellow the mean) it has a negative amplitude•When the wave is in the upwards direction (above the mean) it is positive

Resultant of the interference