Exam Question Help on waves

Here is a video going through typical wave question in an as physics exam. Enjoy. :p

By Ali Mannaraparambil

Electromagnetic spectrum

A prism can split white light into the familiar visible light spectrum, from red to violet. the spectrum shows all the wavelengths of visible light, arranged from the longest wavelength (red ) to the shortest (violet).

 Remember! Visible light is only a tiny part of the entire electromagnetic spectrum.  

The visible spectrum
The symbol for wavelength is the Greek letter lambda  (an upside down y)
the range of wavelengths of visible light is from 400nm (violet light) to 700nm (red light)
for exams make sure you remember a typical wavelength of visible light~ eg. (symbol for lambda )=500nm

Beyond the visible


Above is a diagram showing the electromagnetic spectrum. The electromagnetic spectrum includes wavelengths ranging over many orders of magnitude. it is divided into different regions, but the boundaries between them are not well defined .

For the exams you will need to learn:

• the names of the different regions in the electromagnetic spectrum
• the order they appear in 
• their approximate wavelength ranges

to make this easier i have created a table (below) so that all the information needed is included in the table. make sure you memorize this for the exams.

Region of spectrum	Range of wavelengths (shortest to longest)
Gamma Rays	10-16 to 10-10 m
X-rays	10-13 m to 10-8 m
Ultraviolet	10-8 m to 4x10-7 m (400nm)
Visible light	400nm to 700nm
Infrared	7x10-7 m (700nm) to 10-3 m
Microwaves	10-3 m to 10-1 m
Radio waves	10-1 m to 106 m or more

The Ultraviolet spectrum

The ultraviolet region of the electromagnetic spectrum is sub-divided into three parts:

UV-A - this is the longest wavelength (from 315nm to 400nm). this is the least hazardous form of UV Radiation. however over exposure can cause burning of the skin or even skin cancer. 

UV-B and UV-C have progressively shorter wavelengths, and are more hazardous. 

Sunscreen is used to block these rays so that they cannot penetrate the skin, causing cell damage and disrupting DNA. 

Speed of electromagnetic radiation

All types of electromagnetic radiation travel at the same speed through free space. this is often referred to as the speed of light, symbol C.

the SI system of units, the value of c is defined as C= 299 792 458 ms^-1

for calculations the approximate value of c is C=3x10^8ms^-1

Practical uses for electromagnetic radiation

Below is a table showing the practical uses for electromagnetic radiation , know some of these as you may be asked in exams to provide uses for the electromagnetic radiation.

Electromagnetic radiation	Uses
Gamma Rays	Medical: Destroying dangerous tissue: imaging with tracers. Industrial: sterilising items that may be contaminated with microorganisms; seeing inside solid objects (similar to x-rays).
X-rays	Medical: imaging inside the body. Industrial: seeing inside solid objects, e.g.  To detect cracks.
Ultraviolet	Medical: sterilisation; activating dental fillings. Industrial: sterilisation; visual security markings. Consumer: Reading DVD’s.
Visible light	People: sight. Consumer: reading CD’s.
Infrared	Consumer: remote controls, heating. Industrial: Transmission via optical fibres.
Microwaves	Consume: cooking. Industrial: telecommunications.
Radio waves	Medical: magnetic resonance imaging. Consumer: broadcasting, mobile phones. Industrial: Communicating with spacecraft; telecommunications.

Here is a video explaining how we use electromagnetic wave and how these waves interact.

Questions

1. The red limit of the visible spectrum is at about 700nm. Express this in standard form.
2. In what region of the electromagnetic spectrum does each of the following wavelengths lie?
   1 km, 800 nm, 500 nm, 1 nm
3. which section of the ultraviolet spectrum has the highest frequencies?
4. which of the following gives a good approximation to the speed of light in free space?
   300000 km s^-1, 300000000m s^-1, 300x10^6ms^-1
5. Roughly how many seconds does it take light to travel from the sun to the earth, a distance of 150 million km ?

By Ali Mannaraparambil

Wave Motion

(This is pure Colombian homework. Typed up by hand and not copy-pasted like the rest of the blog).

When people think of waves, they usually think of waves of water, but there are other sorts of waves, such as radio waves and microwaves. These are part of the electromagnetic spectrum (they are electromagnetic waves). If you're still reading this I'm just gonna put this here to show I didn't just copy and paste this. Electromagnetic waves travel travel in free space at 3*10^8 ms-1.

Waves that move away from a source are called progressive waves. The oscillation of a particle is what creates the wave.

Transverse Waves
The direction of the energy transfer is perpendicular to the direction of the oscillations in a transverse wave. The pattern of oscillation looks like a sine wave.

Examples of transverse waves:
-Water waves
-All of the waves in the electromagnetic spectrum
-Waves on a string

Longitudinal Waves
The direction of energy transfer is parallel to the direction of the oscillations in a longitudinal wave. Longitudinal waves are made up of compression (point where the waves squash together) and rarefaction (point where the waves spread out).

Examples of longitudinal waves:
-Seismic P-waves
-Sound waves


QUESTIONS (pg 137, orange textbook):
1.
How do an oscillation and a wave differ? Hint: Think about the motion at one point in space over all time and motion of all points in space at one time.

2.
A longitudinal wave can be represented by a graph of displacement against time or pressure difference against time. Sketch both of these graphs on the same time axis for a sound wave. How are the two waves the same, and how are they different.

By Arjun

Wave Terminology

Terms and symbols used to describe waves.

Wavelength λ , meter(m):

The wavelength of a wave is the smallest distance between two points that have the same pattern of oscillation. It is also the distance the wave travels before the pattern repeats itself. 

Period T , second(s):

The period of a wave is the time for one complete pattern of oscillation to take place at any  point.

Frequency f , hertz(Hz):
The frequency of a wave is the number of oscillations per unit time at any point. 

 Frequency=1/Period.

   

Displacement x , meter(m):

Displacement is the distance any part of the wave has moved from its mean (or rest) position it can be positive or negative.

Phase difference  Φ , rad:

The angular displacement of two points on a wave of identical frequency in terms of how much one wave leads another     

Phase difference concerns the relationship between the pattern of vibration at two points. Two points that have exactly the same pattern of oscillation are said to be "in phase"- there is "zero"

phase difference between them. If the pattern of movement at the two points is exactly opposite to one another, the the waves are said to be in "antiphase", they are half cycle different to one another.

The angle for one complete rotation of the vector arrow is 2π radians.

Waves that are in antiphase are π radians out of phase.

One revolution =circumference of circle

                              radius of circle

2πr  =2π radian

  r

From this we can deduce

360°=2π

180°=π

90°=π/2

     

     

In phase

 
 

Antiphase

By Harshil

Circuit analysis 1 and Circuit analysis 2

EMF and Potential Difference

In any circuit there are components that put energy in to the circuit and components that take energy out. From now on, we will say that any device putting energy into a circuit is providing an electo-motive force (emf) and any device taking it out has a potential difference (pd) across it.

Both emf and pd are measured in volts, V, as they describe how much energy is put in or taken out per coulombof charge passing through that section of the circuit.

The best way to think of them is:

Emf - is the amount of energy of any form that is changed into electrical energy per coulomb of charge.

pd - is the amount of electrical energy that is changed into other forms of energy per coulomb of charge.

Sources of emf:

Cell, battery (a combination of cells), solar cell, generator, dynamo, thermocouple.

Internal Resistance

Cells and batteries are not perfect (what is - apart from the moment your last exam finishes, of course?). Use them for a while and you will notice they get hot.

Where is the heat energy coming from?

It's from the current moving through the inside of the cell. The resistance inside the cell turns some of the electrical energy it produced to heat energy as the electrons move through it.

It is easy to explain if you imagine that each cell is perfect except that for some bizarre reason (probably part of a plot to take over the world, masterminded by Dr Evil) the manufacturers put a resistor in series with the cell inside the casing.

Therefore, inside the cell, energy is put into the circuit by the cell (the emf) but some of this energy is taken outof the circuit by the internal resistor (a pd).

So the pd available to the rest of the circuit (the external circuit, as some questions may refer to it) is the emf minus the pd lost inside the cell:

V = E - Ir

Where:

V = pd across the external circuit (V)

E = emf of the cell (V)

I = current through the cell (A)

r = value of the internal resistance (Ω)

(Ir = the p.d. across the internal resistor)

Note: V is sometimes called the terminal pd as it is the pd across the terminals of the cell

Example 1:

What is the terminal p.d. for a cell of emf 2V and internal resistance 1 ohm when it is connected to a 9 ohm resistor?

Answer:

Just pretend the internal resistance is one of the normal resistors in the circuit. Draw it in the circuit diagram next to the cell so that all the current that goes through the cell also goes through the resistor.

To find V, the terminal pd (or the voltage available to the external circuit), calculate the current, I, for the whole circuit:

Note: V_T and R_T are the voltage and resistance for the whole circuit, including external and internal resistance.

Therefore, the 9Ω resistor gets V = IR = 0.2 x 9 = 1.8V

So this 2V emf cell actually supplies 1.8V to the external circuit.

Example 2:

Now, swap the 9Ω resistor in the last example for a 1Ω resistor.

Answer:

Find V, the terminal pd, using the same method again:

Now the 2V emf cell only supplies 1V to the external circuit!!! The other 1 V is lost making the cell hot. Not very efficient.

Note: You need to consider the internal resistance when deciding if a cell is appropriate to use in a particular circuit. For the greatest efficiency the external resistance must be much greater than the internal resistance of the cell. However, for the maximum power to be delivered to the external circuit the internal resistance must be equal to the resistance of the external circuit, although the cell will only be 50% efficient.

High and Low Voltage Power Supplies

Power supplies which deliver low voltages and higher currents, like a car battery, need to have a low internal resistance, as shown above. High-voltage power supplies that produce thousands of volts must have an extremely high internal resistance to limit the current that would flow if there was an accidental short-circuit.

Finding Internal Resistance Experimentally

As V = E - Ir, if you plot a graph of terminal pd, V, against current, I, the gradient of the graph will be equal to the internal resistance of the cell. (negative because the graph slopes down)

By recording values of current and terminal pd as the external resistance changes you can plot the graph and find the internal resistance and the emf of the cell.

If there is more than one cell in series the internal resistances of the cells must be added.

Parallel circuits

Putting electrical components in parallel is a common practice.

House circuits are also parallel. This is an example of bulbs in a parallel circuit:

 

This way you can turn one light bulb on at a time if the main switch is on. If one of the bulbs blows the other will still be working because the circuit will still be complete. That is why we don’t place house circuits in series because if one bulb blows, everything will turn off.

Kirchhoff’s second law:

Kirchhoff’s second law is an electrical application of the law of conservation of energy. It states that:

“In any closed loop in a circuit the sum of the e.m.f.s is equal to the sum of p.d.s”

Remember: e.m.f. is the energy per unit charge transferred into electrical energy.

p.d. is energy transferred per unit charge from electrical energy.

 

Resistors in parallel:

 

Circuit resistance when all items are switched on: =supply p.d / total current.

=230/1.15A=200Ω

Total resistance in parallel circuits:

1/RT= 1/R1 + 1/R2 + 1/R3.....

 

 Sajeel