Physics (Wave Phenomenon)

GREASE THOSE WHEELS (PHYSICS)

#1 WAVES PHENOMENON

• describe what is meant by wave motion.
• show understanding and use of terms such as displacement, amplitude, phase difference, period, frequency, speed and wavelength.
• derivation and usage of the wave equation; v = fλ
• show understanding that energy is transferred in a progressive wave.
• recall the relationship intensity of a wave is ∝ (amplitude)^2
• compare transverse and longitudinal waves.
• analyse graphical representation of transverse and longitudinal waves.
• show understanding of the term polarization and its association with transverse waves.
• determine the frequency of sound using a calibrated c.r.o
• determine the wavelength of sound using a stationary wave.
• recall the order of the electromagnetic spectrum and the variation in frequency and wavelength as we move along it from radio waves to gamma waves.

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Waves and its relative concepts are probably the most dreaded part of your physics syllabus but with a little effort put in, they become as easy as everything else that you found difficult.
Lets start with the most basic question, what is wave motion?

Just look at the photograph on the left...it is the most common visual to let you grasp the concept of wave motion. Your drop a pebble in a pond and it creates some sort of disturbances around it that travel away from the point of impact.These are waves which transfer the energy from the collision with the pebble to other parts of the liquid without a net movement of molecules. This movement thingy can be understood by assuming yourself as a pond-skater or simply a leaf that is in the path of the travelling waves, what will happen to you as the waves approach and collide with you? yep! nothing but a little bit of bouncing!!! The same is the case with water molecules, they oscillate about their position in the liquid without any net displacement. So, conclusively, wave motion can be defined as..

"the motion or spread of a disturbance, mostly by transfer of energy, within a medium without a net displacement of that medium's molecules"

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Now let's move on to some of the basic stuff regarding waves...

1. Displacement is the distance traveled by the wave away from the source of propagation or in the direction of motion.
2. Amplitude is the maximum displacement of a particle from its mean position in a wave (distance y0 in the above illustrated figure)
3. Period is the time taken in seconds for a particle to complete one whole oscillation or the time consumed (s) in the generation of one complete wave.
4. Frequency it is the number of complete waves produced per second and thus is the inverse of the time period. Its unit is Hz or /s.
5. Speed of a wave is the rate of change of displacement. (unit: m/s)
6. Wavelength (symbol: lambada, λ) is the distance difference between corresponding points (like, C and E, A and C, B and D in the figure above) on a wave in the direction of motion. (unit: metre)
7. Phase difference in wave terminology, occurs when two particles oscillating with the same frequency but are in different phases in a wave cycle or when two different waves have the same frequency but different starting points. Think of it as you and a friend of yours are running to the finish line in a 500m sprint with the same velocity but different starting points. On the way, say, you pass an old man and your friend passes the old man 10 seconds after you so you say that you lead your friend by 10 seconds or your friends is 10 seconds behind you. Same is the case with waves but we measure the difference in their relative positions at a time interval in degrees or radians. Another point to notice is that transverse waves can usually be divided into 4 equal parts [two symmetrical parts from the crest and two from the trough] so each part makes up 1/4 of the wave and thus 90 degrees of the complete 360 degree wave cycle.

• Waves or particles on a wave that have a phase difference of 180 degrees are said to be in anti-phase. That is for example when at time t seconds the first wave is in the crest phase the second wave will be in the trough phase of the wave cycle.
• Waves out of phase have a difference less than 180 degrees between them. It may be constant or increasing/decreasing.
• Waves or particles on a wave that are in-phase i.e, having complimentary motion have zero phase difference between them regardless of their amplitude.
• Wave sources that are coherent have constant phase difference between them.
• Waves that have a whole number path difference or time interval difference between them are usually in-phase.

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Now let us get to the heart and soul of wave problems; the wave equation.
Its derivation is very simple...
Consider a wave moving with velocity v and having a time period T, by applying s=vt we get the equation...
λ=vT.
Replacing T by its inverse f aka frequency we get...λ=v/f and finally...

      v=fλ       

-------The Universal Wave Equation-----

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Now lets move to the concept of progressive and stationary waves...as far as progressive waves are concerned you should grasp their defination quite well 'coz its one of examiner's favourite...

"A progressive wave transfers energy from one place to another via its oscillations."

A clear example of a progressive wave are the UV Rays from the sun. Whilst playing outdoors during afternoons you can feel the energy being transfered to your skin in the form of heat. Another example can be a  whip (aaaooo!!)....you can ask about the energy transferred from the horses...=P...and they won't like you asking about it!!!
Moreover in a progressive wave...

• Adjacent particles have equal amplitude.
• All particles oscillate.
• Neighboring particles are never in phase...for the particles on a transverse wave to be in phase they should be separated by atleast one wavelength.
• Energy is transferred in the direction of motion.

 "A stationary wave doesn't transfer energy from one place to another by oscillates about its fixed position."

A super-useful and most frequently given example of a standing or stationary wave are the strings on an acoustic instrument like a violin, guitar, bonjo or a sitar. Once plucked, the strings oscillate about their fixed position with no uniform transfer of energy as the ends are fixed, this fixation also results in the continuous reflection of wave up and down and the occurrence of interference which we will cover ind detail in the future.
To summarise, in a stationary wave...(refer to the figure above)

• Adjacent particles (in every λ/4)  never oscillate with the same amplitude.
• Energy is localised to every particle without any energy transfer as seen in a progressive wave, although some energy is transfered to surrounding air molecules which results in a sound wave being generated.
• Particles are in-phase for every λ/2 of the wave and are in antiphase for the other half.
• Not all particles oscillate in a stationary wave, some are permanently at zero displacement (nodes, shown in red dots in the figure above) while the antinodes bare the maximum displacement \ amplitude  regions of a stationary wave weather positive or negative. (Moreover for a stationary wave, λ can be defined as the distance between two successive nodes or antinodes).

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Intensity of a wave is the amount of energy a wave transfers in the direction of motion per unit of area per unit of time. Unit being Joules/m squared/second or simple (J/s = Power) Watts/m squared.

In our course these two relationships of Intensity with other physical quantities should be known...

• Intensity ∝ Amplitude squared (the more the amplitude the more the energy transfered). Simple example...the more the volume of the T.V set the more your ears get blasted off!!
• Intensity ∝ 1/Area (the more the area the lesser the intensity). Try moving away from a computer speaker...you get lesser and lesser sound because the wave have to cover more distance to reach you and dissipate more energy in the meantime.

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A transverse wave is the one in which motion of the particles involved is perpendicular to the motion of the wave. Transverse waves are made of alternating crests and troughs. They can be medium-independent and can travel through space. Tranverse waves oscillate in two dimensions and thus can be polarized. The whole of the electromagnetic spectrum is made up from types of transverse waves.

While a longitudinal wave involves motion of oscillating particles, parallel to the motion of the wave. Longitudinal waves are made of alternating regions of compressions(high density and high pressure) and rarefactions(low density and low pressure or 1 atm). They are medium-dependant and cannot travel through space. Longitudinal waves cannot be polarized as their oscillations are limited to only one dimension. Sound waves and seismic waves are well known examples of longitudinal waves.

Now let us look at their graphical representations. (Pictures Courtesy...Oxford University Press)
Remember it is helpful to imagine these graphs as snapshots of the wave at that instant.
Their are two main graphs that we will consider. Distance-Time and Distance-Displacement.
For a transverse wave the displacement-distance graph (which can also be thought of as a displacement-position graph which shows the relative displacements of oscillating particles at different positions within a wave cycle) is merely its photograph at that instance useful for finding out amplitude, wavelength etc.

It is a different case for a longitudinal wave where it cannot be imagined as a snapshot but still can be used to find out where compression is occurring and where rarefaction and subsequently the wavelength can be found out. I think it is safe to say in the lgiht of the following graph that compression occurs in the +ive to -ive direction while rarefaction occurs in the -ive to +ive direction.

Now let us take a look at displacement-time graph which depicts the displacements of one particle at various instants of time. And thus can be used to find out the time period, amplitude and from the time period, the frequency of the wave.

Conclusively, I would like to mention that the maximum speed of an oscillating particle is at the equilibrium posiiton while the maximum acceleration of a particle is at the maximum displacment of the particle in a displacement-time and acceleration-time graph respectively. Moreover when asked about the direction of velocity of an oscillating particle in a wave, you should keep in mind that the particles take turns in becoming crests and troughs and therefore every crust has to go down and every trough has to move up so while keeping in view the motion of the wave you can easily tell the direction of velocities of particle(s). Classic! aint it?
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Now we come to the term polarization and what the hell is it??=P
Basically at the core of it is a simple fact that light waves oscillate in a multitude of directions, why this is so is beyond the scope of our syllabus but at our level, simply put, light waves oscillate in two dimensions or two planes, one vertical (electric) and the other horizontal (magnetic). So a light waves that oscillates in only one of these planes is called polarized light.
A light is usually polarized by the use of a Polaroid filter which allows light of only a single polarity to pass through. This concept is used in sunglasses and 3-D screening of movies. As the light is polarized by a Polaroid filter, it is important to notice that its intensity is reduced, or more specifically halved (if u have worn a pair of sunglasses then you will know what I am talking about =)). A simple illustration is given by the figure below.

A point to remember is that only transverse waves can be polarized and polarization doesn't effect longitudinal waves.

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Our next stop is the Electromagnetic Spectrum...
The entire electromagnetic spectrum consists of seven different types of radiations. Lets have a look at it as a whole first....

You just have to remember the wavelength of these as frequency can be taken out be using the wave equation keeping in view that all waves in an electromagnetic spectrum travel at 3 x 10^8 m/s. And also the order of increasing wavelength for different colours of light VIBGYOR. Now lets break it down to the components...

• Radio Waves: 10^3m : 10000 Hz: Broadcasting, Wireless Communication
• Microwaves: 10^-2m : 10^8 Hz: Microwave Ovens
• Infrared: 10^-5m : 10^12 Hz: Remote Controlling, Thermal Imaging.
• Visible Light: 10^-6m : 10^15 Hz: Seeing, Optical Imagery.
• UV Rays: 10^-8m: 10^16 Hz: Checking for forfeited bank notes.
• X-Rays: 10^-10m: 10^18 Hz: Medical Examinations.
• Gamma Rays: 10^-12m: 10^20 Hz: Sterilization.

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Thats it for this stuff!! Do leave a comment if you have some suggestions or just to say thanks!!

org. date 4/22/10 @ 6:19 PM