 # Topic 4.4 Wave characteristics. Learning outcomesTeacher’s notes 4.4.1Describe a wave pulse and a continuous progressive (travelling) wave. Students should.

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Topic 4.4 Wave characteristics

Learning outcomesTeacher’s notes 4.4.1Describe a wave pulse and a continuous progressive (travelling) wave. Students should be able to distinguish between oscillations and wave motion, and appreciate that, in many examples, the oscillations of the particles are simple harmonic. 4.4.2State that progressive (travelling) waves transfer energy. Students should understand that there is no net motion of the medium through which the wave travels. 4.4.3Describe and give examples of transverse and of longitudinal waves. Students should describe the waves in terms of the direction of oscillation of particles in the wave relative to the direction of transfer of energy by the wave. Students should know that sound waves are longitudinal, that light waves are transverse and that transverse waves cannot be propagated in gases. 4.4.4Describe waves in two dimensions, including the concepts of wavefronts and of rays. 4.4.5Describe the terms crest, trough, compression and rarefaction. 4.4.6Define the terms displacement, amplitude, frequency, period, wavelength, wave speed and intensity. Students should know that intensity ∝ amplitude2. 4.4.7Draw and explain displacement–time graphs and displacement–position graphs for transverse and for longitudinal waves. 4.4.8Derive and apply the relationship between wave speed, wavelength and frequency. 4.4.9State that all electromagnetic waves travel with the same speed in free space, and recall the orders of magnitude of the wavelengths of the principal radiations in the electromagnetic spectrum.

Waves and Oscillations Oscillation: the vibration of an object Wave: can be a pulse wave or a continuous progressive (travelling) wave. o Pulse: single oscillation or disturbance o Continuous traveling wave: succession of oscillations (series of periodic pulses) Both pulses and traveling waves: transfer energy though there is no net motion of the medium through which the wave passes. o A wave transfers energy without a transfer of matter

TRAVELLING WAVES Definition: A travelling wave (or “progressive wave”) is one which travels out from the source that made it and transfers energy from one point to another. Students should understand that there is no net motion of the medium through which the wave travels.

Transverse vs longitudinal Types of Traveling Waves

Transverse vs. longitudinal waves Transverse waves are when the particles in the medium vibrate at right angles to the direction of energy transfer Longitudinal waves are when the particles (of the medium) vibrate in the same direction as the direction of energy transfer; Displacement of particles Direction of wave/energy transfer Displacement of particles Direction of wave/energy transfer

Transverse wave

Transverse waves Examples of transverse waves: light, violin and guitar strings, ropes, earthquake S waves Transverse waves cannot propagate in a gas or a liquid because there is no mechanism for driving motion perpendicular to the propagation of the wave http://www.acoustics.salford.ac.uk/f eschools/waves/bungyvideo.htm http://www.acoustics.salford.ac.uk/f eschools/waves/wavetypes.htm

http://www.acoustics.salford.ac.uk/feschools/waves/guitarvideo.htm

Longitudinal waves Sound waves and earthquake P-waves are longitudinal

Loudspeaker

Be a Thinker!

Waves in Two Dimensions

Wavefronts and rays Ray: direction in which wave (energy) is travelling; Wavefront: line joining neighbouring points that have the same phase /displacement. The distance between two successive wavefronts is one wavelength The ray is always normal to a wavefront;

Describe waves in two dimensions, including the concepts of wavefronts and of rays. Energy is transferred in 2 dimensions Watch the wavefront(s) propagate http://www.acoustics.salford.ac.uk/f eschools/waves/dripvideo.htm

Wavefronts and rays Rays show the direction of travel of the energy. The wavefronts are where the crests of the waves are. The rays are always at 90 deg to the wavefronts. rays Wavefronts

Characteristics of a Wave.

Longitudinal waves v Compression is a term used in connection with longitudinal wave and refers to the region where the particles of the medium are "bunched up".  High density  High pressure v Rarefaction is a term used in connection with longitudinal waves referring to the regions where the particles are "stretched out".  Low density  Low pressure

Longitudinal waves v The wavelength will be equal to the distance between successive points of maximum compression and successive points of maximum rarefaction. v The compression is the region in which the molecules of the air are pushed together v The rarefaction is the region where the molecules move apart.

Transverse waves Crests Troughs

Displacement graphs This graph represents a snapshot of the vibrating medium (ex: string) at a specific instant of time. It shows the displacement of each particle of the medium away from the equilibrium position at that specific instant of time The information that can be deduced from this graph: The amplitude of the wave The wavelength The relative position of each particle in the medium at this specific time

Displacement graphs This graph represents the of the variation of the displacement of one specific particle of the medium away from the equilibrium position with time The information that can be deduced from this graph: The amplitude of the wave The period of the wave

Define the terms displacement, amplitude, frequency, period, wavelength, wave speed and intensity WAVELENGTH - the distance from one crest to another or one trough to another. (In fact generally from any point on the wave to the next exactly similar point i.e. 2 consecutive points in phase) FREQUENCY - the number of vibrations of any part of the wave per second. The bigger the frequency the higher the pitch of the note or the bluer the light AMPLITUDE the maximum displacement that any point on the wave moves from its mean position. The bigger the amplitude the louder the sound, the rougher the sea, or the brighter the light

More terms Period (T) The time it takes for one complete cycle of the wave. Displacement (x) How far the “particle” has travelled from its mean/equilibrium position. Wave speed (v) The speed at which the wavefronts pass a stationary observer Intensity (I) The power per unit area that is received by an observer. Students should know that intensity ~ amplitude 2

Derive and apply the relationship between wave speed, wavelength and frequency. Wave speed (v) = frequency (f) x wavelength ( ) in m/s in Hz in m The wave equation relates the speed of the wave to its frequency and wavelength:

More about the speed of the Wave  The Speed of waves only depends on the nature and the properties of the medium w Water waves do travel faster in deeper water w Light travels slower in more optically dense material  The frequency of a wave depends only on the source producing the wave w It will therefore not change if the wave enters a different medium or the properties of the medium change  The wavelength changes according to the wave equation V=f λ  Example: when water waves approach the shore (shallow water), velocity decreases, frequency remains constant, so, wavelength decreases. (Tsunami only appears in shallow water)

Be a Thinker! Which of the following best describes the wave speed of a progressive wave travelling through a medium? A.The maximum speed of the vibrating particles of the medium B.The average speed of the vibrating particles of the medium C.The speed of the medium through which the wave travels D.The speed of transfer of energy through the medium

Be a Thinker!

Intensity Source: http://www.physicsclassroom.com/Class/sound/u11l2b.cfm

Intensity The diagram at the right shows that the sound wave in a 2-dimensional medium is spreading out in space over a circular pattern. Since energy is conserved and the area through which this energy is transported is increasing, the power (being a quantity that is measured on a per area basis) must decrease. The mathematical relationship between intensity and distance is sometimes referred to as an inverse square relationship. The intensity varies inversely with the square of the distance from the source. So if the distance from the source is: –doubled (increased by a factor of 2), then the intensity is quartered (decreased by a factor of 4). –Similarly, if the distance from the source is quadrupled, then the intensity is decreased by a factor of 16. Source: http://www.physicsclassroom.com/Class/sound/u11l2b.cfm

Electromagnetic waves

Frequencies of Regions (Hz) Gamma Rays >10 21 X-rays 10 17 - 10 21 Ultraviolet 10 14 - 10 17 Violet 7.5 x 10 14 > Visible > Red 4.3 x 10 14 Infrared 10 11 -10 14 Microwaves 10 9 -10 11 Radio and TV < 10 9

The Different Regions v In the context of wave motion, common properties of all parts of the electromagnetic spectrum are w all transverse waves w all travel at the speed of light in vacuum (3.0 x 10 8 ms -1 ) w all can travel in a vacuum

Sources of Regions w Gamma – certain radioactive material’s nuclei w X-rays – by firing an electron stream at a tungsten metal target in a highly evacuated tube. w Ultraviolet – the Sun, ultraviolet lamp w Visible – hot bodies w Infrared – the Sun (heat), hot bodies w Microwaves – Ovens, communication systems w Radio and TV – transmitter stations, Azteca TV

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