Long time since I’ve touched this..

I just got a comment, comments are rare for me. It regards physics. I’ve not touched physics in a very long time, but I’ll try to answer it as best as possible.

“how does the variation of amplitude with distance from the source differ for a progressive wave and a stationary wave? i hope that u wud find me an ans for this question as soon as possible”

(I’ve used standing wave instead of stationary wave because that’s what I’m used to, and the fact that I’m not sure if it’s stationary or stationery and can’t be bothered googling.)

Amplitude is the maximum displacement from equilibrium that a point on the wave can have. In a progressive wave, every point on the wave from the source to the end of the wave has the exact same amplitude, as if you consider each point, it is moving up and down the same amount as the point next to it, but is slightly out of phase. Thus, the amplitude from the source in a progressive wave is a constant value.

It’s different for standing waves, because they have nodes and antinodes. At antinodes, they have an amplitude of zero. At nodes, they have their maximum amplitude, and their amplitude is different for all points between the nodes and antinodes. The source will usually [always? Can't remember {No, not always, because you can make a standing wave with a slinky by having the node at one end.}] be at an antinode. So in a standing wave, from the source, the amplitude is not a constant. From the source, the amplitude will increase (in a sinusoidal manner(?)) until the first node, and then decrease (in a sinusoidal manner(?)) until the second antinode. This then repeats based on which harmonic the standing wave is at (ie. how many nodes it has).

So to sum up: The amplitude from the source in a progressive wave is a constant value, whereas in a standing wave the amplitude varies. From the source, the amplitude will increase in a sinusoidal manner until the first node, and then decrease again to zero amplitude in a sinusoidal manner to the next antinode.

To put it simply though, if the question’s a lot easier than I’m making it out to be, “Progressive waves have a constant amplitude while in a standing wave, the amplitude is variable depending on where the point lies between a node and an antinode.”

I’d illustrate this with graphs and charts and all manner of flashy things, but I’m far too lazy busy for that.

I hope that this answers your question. Actually, I hope more that I’m right, it’s been a while since I did this kind of thing. It sounds right, anyway. The kind of thing I’d say.

Physics Revision 12 – The Photoelectric Effect

Photoelectric Effect

The Photoelectric Effect demonstrates that waves can sometimes behave as particles, in Quantum Physics. This is what Einstein won his Nobel Prize for.

A photon is a ‘quantum of EM radiation’

It involves exposing a piece of metal to electromagnetic radiation. If the energy of the photons in the radiation is high enough, electrons will be given off from the metal. As electrons (Negative charge) are being given off, the resulting metal will have a positive charge.

E = h f
E = [Phi] + 1/2 m v[max]^2
P = E n

P = Power
n = Number of photons
E = Energy of photon
h = Planck’s Constant [6.63x10^-34]
f = Frequency of electromagnetic wave
[Phi] = Work function, the minimum energy required to emit electrons.
1/2 m v[max]^2 = The maximum kinetic energy that the photoelectron has upon leaving the metal.

m = mass
v = velocity

The threshold frequency is the frequency when:-
hf = [phi] (ie. the photoelectrons only just leave the metal). If hf < [phi], no photoelectric effect is observed.

1 electron Volt (eV) = 1.6×10^-19 J. Work function is normally measured in eV, as it makes numbers easier to manage.

The intensity of electromagnetic radiation affects the NUMBER OF PHOTONS that hit the metal, thus the number of electrons emitted
The frequency of electromagnetic radiation affects the ENERGY OF PHOTONS that hit the metal, thus the maximum kinetic energy of electrons emitted.

Electromagnetic waves can behave as particles or as waves.

Waves:-
- Shows diffraction
- Diffracted by slits
- Diffraction noticable when size of gap ~ [lamda]
- Shows interferences
- Shows polarisation
- v = f [lamda]

Particles:-
- Interaction of EM waves with matter
- Energy of photons given by E = hf
- E = energy of photon, f = frequency, h = 6.63×10^-34
- Photoelectric Effect
- One-to-one interaction between photon and electron
- Energy is conserved (hf = [Phi] + 0.5mv^2)
- Frequency affects the energy of photons

Physics Revision 11 – Electromagnetic Waves

Electromagnetic Waves

Gamma Rays – Used in radiotherapy
X-Rays – Used for taking pictures of skeleton
Ultra-Violet – Used for tanning [May cause cancer]
Visible Spectrum – The colours that the human eye can see
Infra Red – Used in TV remote controls
Microwaves – Used in mobile phones
Radio Waves – Used in communication

All electromagnetic waves:-

- Travel at the speed of light (3.0×10^8)
- Travel through a vacuum
- Have oscillating electric and magnetic fields
- Are all transverse waves, and thus can be polarised
- Show diffraction, reflection, refraction, and interference
- Consist of photons

Wavelengths:-

Gamma = < 10^-11 m
X-Ray = 10^-9 -> 10^-11 m
Ultraviolet = 4×10^-7 -> 10^-9 m
Visible = 7×10^-7 -> 4×10^-7 m
Infrared = 0.0001 -> 7×10^-7 m
Microwave = 0.1 -> 0.0001 m
Radio = > 0.1 m

A photon is a particle of light. The energy of a photon depends on it’s frequency.

E = h f

E = Energy of the photon (Joules)
h = Planck’s Constant (6.63×10^-34)
f = Frequency

Physics Revision 10 – Magnets And Stuff

Magnets and stuff

A current carrying conductor has a magnetic field around it, in concentric circles.  To work out the direction of the field, use the Right Hand Grip rule.  Hold your right hand in a ‘thumbs up’ position, where the direction of the thumb represents the direction that current is flowing.  The direction that the other fingers wrap round is the direction of the magnetic field.  The field lines spread out more the further away they are from the wire.

To find out the force experienced by a current carrying conductor in a magnetic field, we use Fleming’s Left Hand Rule.  Hold the first two fingers and the thumb of the left hand at right angles to each other.  The thumb represents the direction of the force, the first finger represents the direction of the magnetic field, and the second finger represents the direction of current flow.

Magnetic Flux Density is the force on a conductor, per unit length, carrying a unit current and placed perpendicular to the magnetic field.

F = BIL

F = Force (Newtons)
B = Magnetic Flux Density (Tesla)
I = Current (Amps)
L = Length of conductor in field (Metres)

A solenoid is a circular coil of wires that is carrying a current.  The magnetic field goes through the middle of the solenoid, and round the outside.  By carrying out the Right Hand Grip rule at any point on the solenoid, it is possible to determine which way the field goes through the coil.

The ampere is an important electrical unit that is based on the force experienced between two current-carrying conductors.

Physics revision 9 – EMF & Internal Resistance

EMF & Internal Resistance

EMF is ‘electromotive force’.  This is the energy converted from chemical energy to electrical energy. (The energy gained by charge)
PD is ‘potential difference’.  This is the energy lost by charge.

Batteries have an internal resistance.  This basically acts like a small series resistor, caused by the chemicals inside the battery.  If Vs and I are known, then the total resistance in the circuit can be calculated (V=IR).  Take away any known resistors, and the internal resistance will be left.

If internal resistance is known, the voltage across the terminals of the battery can be calculated with potential divider formula.

The larger the value of other resistors in the circuit, the less effect the internal resistance has.

Physics Revision 8 – Potential Dividers

Potential Dividers

<Insert notes about Potential Dividers here. I know all about Potential Dividers from Electronics anyway, and this post was originally lost about 40 minutes ago by a firefox crash, and I can’t be bothered rewriting them.

So… Yes, pretend there’s notes here.>

Physics Revision 7 – Resistivity

Resistivity

How does the resistance of a component change with the voltage across it?

- Metal conductor – Resistance stays constant for all voltages [Assuming temperature is constant]
- Filament lamp – Contains tungsten, which heats up.  Resistance is constant to about 2V, as the temperature is constant, and then increases in a curve as the temperature increases. Tungsten is long, so is coiled up inside the lamp to fit.
- Silicon diode – Resistance is infinite for all negative voltages, and for all positive voltage up to 0.7V.  At 0.7V, resistance drops quickly and it begins conducting.  A diode is a semiconductor, meaning it only conducts some of the time.

A metal conductor is an Ohmic conductor, ie. it follows Ohm’s Law.
A filament lamp is non-ohmic.
A silicon diode is non-ohmic.

When the temperature increases, the resistance increases, because the atoms in the conductor vibrate more, and so the electrons collide with the atoms more frequently.

What does the IV graph of a component look like?

- Metal conductor – Straight line, constant gradient, through the origin.
[The resistance is constant, I is directly proportional to V]
- Filament lamp – Curve, through origin, looking like “r”.
[R increases as V.I increases, because the temperature increases, and the filament gets hotter, causing the resistance to increase]
- Silicon diode – 0 to 0.7V, then curves up steeply.
[When V<0.7, R is very large.  When V>0.7, resistance decreases, getting very small.

R = [Rho] L / A
[Rho] = RA/L
A = [pi]r^2

R = Resistance
[Rho] = Resistivity.  Resistivity is the resistance of a conductor of unit cross-sectional area per unit length.
L = Length
A = Area
r = Radius of wire
[pi] = 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679…..

Physics revision 6 – Basic Electricity

Basic Electricity

Equations:-

V = IR
Q = IT
P = IV
P = IIR
P = VV/R
W = ITV
W = PT
W = QV
Q = EN

W = Work (Joules)
P = Power (Watts)
T = Time (Seconds)
Q = Electrical Charge (Coulombs)
I = Current (Amps) – Measured with an ammeter in SERIES with the component
V = Voltage (Volts) – Measured with a voltmeter in PARALLEL with the component
R = Resistance (Ohms)
E = Electron charge (1.6×10^-19)
N = Number of electrons flowing

Current = The flow of charged particles
Resistance = Potential difference per unit current (V/I)
One Coulomb is the charge flowing past a point in 1 second when the current is 1A.

Ohm’s Law states that I is proportional to V in a metallic conductor at constant temperature.  A metallic conductor obeys Ohm’s Law, whereas a diode or a thermistor does not.

In metal, charged particle responsible for current = ELECTRON
In an electrolyte (Conducting solution), charged particle responsible for current = ION

In a circuit, conventional current flows from + to -, BUT the electrons flow from – to +.

When resistors are connected in series, the total resistance is R1 + R2 + R3 etc. = Rt
When resistors are connected in parallel, the total resistance is (1/R1) + (1/R2) + (1/R3) etc. = (1/Rt)

In a bulb, Electrical energy changes to Heat & Light energy.

Energy is commonly measured in “kWh”, which is the power used in kilowatts, multiplied by the number of hours that it is used for.  Electricity companies charge customers for how many kWh they use.

1kWh is the energy transformed by 1kW device in a time of 1 hour.  W = PT. 1 kWh = 1000 x 3600 = 3.6×10^6 joules
1eV is the energy transformed by an electron travelling through a PD of 1 V. W = VQ. 1 eV = 1.6×10^-19 joules

kWh is useful when dealing with large amounts of energy. (Domestic use, Electrical bills)
eV is useful when dealing with small amounts of energy. (Photons, Atomic physics, Nuclear physics)

Kirchoff’s First Law states that the sum of the currents going into a junction is equal to the sum of the currents going out of the junction.
Kirchoff’s Second Law states that the sum of the electromotive force around a closed loop is equal to the sum of the PDs around the same loop.  This is a consequence of the conservation of energy.

Physics revision 5 – Standing Waves

Standing Waves

A progressive wave is a wave that transfers energy.

Standing waves are waves that have nodes and antinodes.

A node is a point on the wave that has 0 amplitude.
An antinode is a point on the wave that has a maximum amplitude.

When a guitar string is plucked, it causes a standing wave, the ends are nodes and the point in the centre is an antinode.

A progressive wave is a wave that looks to be moving.

Similarities between Progressive and Standing waves…
- The particles vibrate in the same direction (For a standing sound wave, in the same direction of the wave. For a standing transverse wave, at 90 degrees to the direction of the wave)
- Both standing and progressive waves involve particles vibrating, amplitude, frequency, wavelength, etc.

Differences between Progressive and Standing waves…
- In a progressive wave, all particles have the same amplitude, but particles have different amplitudes in a standing wave.
- In a standing wave, there are particles that don’t move, but all particles in a progressive wave move.
- Phase difference exists between vibrations of neighbouring particles in progressive waves, but no phase difference between vibrations of neighbouring particles in a standing wave.
- A progressive wave transfers energy, but a standing wave doesn’t.

In an air column…
Node at the bottom, antinode at the top [fundamental]
Node at the bottom, antinode 1/3 of the way up, node 2/3 of the way up, antinode at the top [2nd harmonic]
–Etc.

By blowing across the top of an air column (Such as a pipe), a longitudinal standing wave is formed inside the air column. (This is how pan pipes work etc)

At the fundamental, the wavelength of the sound wave is 4x the length. (Wavelength in a standing wave is N-A-N-A-N)

In an open pipe, both ends MUST be an antinode. Therefore, in an open pipe, the standing wave goes (A-N-A). This means that the wavelength of a standing wave for an open pipe is 2x the length.

Standing waves on a string are caused by a transverse wave moving along the string, reflecting off the other side, and superposing with the original wave to create points of zero amplitude. (May also occur with microwaves – if they are fired at a reflective surface, they will superpose with the original wave to cause periods of maxima and minima along the line of the wave.

Also see http://mindez.wordpress.com/2008/09/08/long-time-since-ive-touched-this/ for an idea of how and why the amplitude differs between progressive and standing waves!

Physics revision 4 – Interference

Interference

Superposition is the vector addition of two waves.

Interference occurs due to two waves acting on the same point and superposing.  Interference can be constructive, ie. the two waves are both at a peak, so the superposed output is high, or interference can be destructive, ie. one wave is at a peak when the other is at a trough, so the resultant superposed wave is small.

Total destructive interference occurs when wave sources are of the same amplitude, and in antiphase.  This means that the result of the vector addition of the two waves gives an output with no amplitude.

If two waves have the same amplitude and are directly in anti-phase, they will always interfere destructively to give a superposed wave with 0 amplitude at all points.

If two waves have the same amplitude and are directly in phase, they will always interfere constructively to give a superposed wave with double amplitude, with the same frequency/wavelength.

In order to produce a good interference pattern, the sources of the two waves have to be coherent.  Coherent means that the two waves have a constant phase difference.

To produce an interference pattern, a double slit experiment may be used.  This involves:-

Light source -> Double slit -> Screen

[lamda] = frequency of light source
x = Fringe separation, the distance between two light fringes on the screen
D = Distance from slit to screen
a = distance between slits

x = ([lamda] D) / a

x & a can be measured using a travelling microscope.
D can be measured using a metre ruler

Likely values..

x = 10 mm
D = 5.0 m
a = 1.0 mm

O – O – O – O – O

At the middle O, path difference = 0
At the first – from the middle, path difference = 0.5[lamda].
At the next O, path difference is [lamda].
Next -, 1.5[lamda]
Next O, 2[lamda]

etc.

Where a bright fringe is observed, constructive interference occurs, and the path difference is a whole number n wavelengths.  Where a dark fringe occurs, destructive interference occurs, and the path difference is n+0.5 wavelengths.