Wave Properties

Measuring Waves:

The frequency of a wave is the number of complete waves passing a point per second.
The amplitude of a wave is the maximum displacement of a vibrating particle.
The wavelength of a wave is the least distance between two adjacent vibrating particles with the same displacement and velocity at the same time.

The higher the frequency of a wave, the shorter its wavelength. The equation for
wave speed = frequency x wavelength

Wave Properties

Reflection - Straight waves directed at a certain angle to a hard flat surface reflect off at the same angle. The angle between the reflected wavefront and the surface is the same as the angle between the incident wavefront and the surface. The angle between the incident ray and the mirror is equal to the angle between the reflected ray and the mirror.

Refraction - When waves pass across a boundary at which the wave speed changes, the wavelength also changes. The direction of the refracted waves is closer to the normal than the directed of the incident waves. An example is, a light ray directing into a glass block. The light ray changes direction when it crosses the glass boundary. This happens because light waves travel more slowly in glass than in air.

Diffraction - This occurs when waves spread out after passing through a gap or around an obstacle. The effect can be seen in a ripple tank when straight waves are directed at a gap. The narrower the gap, the more the waves spread out. The longer the wavelength, the more the waves spread out.

Matters and Radiation

Inside the atom

Every atom contains a positively charged nucleus composed of protons and neutrons and electrons surrounding the nucleus. The word nucleon is used for a proton or a neutron in the nucleus. The table below shows the charges and mass of protons, neutrons and electrons.

 

Isotopes are atoms of the same elements with the same number of protons but different number of neutrons.

 

The specific charge of a charged particle is defined as its charge divided by its mass.

 

For example, a charged particle has a charge of 1.60 x 10^-19 C and a mass of 1.67 x 10^-27  kg.

Therefore, the specific charge is : 1.60 x 10^-19 C /1.67 x 10^-27  kg = 1.76 x 10^¹¹   Ckg^-1

 

Stable and unstable nuclei

 

A force that holds a stable nuclei is called the strong nuclear force, as it overcomes the electrostatic force of repulsion between the protons in the nucleus and keeps the protons & neutrons together.

 

Alpha radiation consists of alpha particles which comprise of 2 protons and 2 neutrons. Therefore its mass number is 4. As the nucleus emits an alpha particle, its nucleon number decreases by 4 and its atomic number decreases by 2.

 

 

For example:

 







Gamma radiation is electromagnetic radiation emitted by an unstable nucleus. It can pass through thick metal plates. It has no mass and no charge.

 

 

Photons

 

All electromagnetic waves travel at the speed of light (c), which is 3.0 x 10^⁸ .

Electromagnetic waves are emitted by a charged particle when it loses energy. They are emitted as short 'bursts' of waves, each burst leaving the source in a different direction. Each burst is a packet of electromagnetic waves and is referred to a photon. This is the emission of electrons from a metal surface when light is directed at the surface.

 

photon energy E = hf

 

h=Planck's constant (6.63 x 10^^-34 Js)

 

Example: Calculate the frequency and the energy of a photon of wavelength 650nm

 

h = 6.63 x 10^^-34 Js

c = 3.00 x 10^^-8  ms^^-1

 

 

 

 f = (3.00 x 10^^-8  ms^^-1 ) / (650 x 10^^-9 ) = 4.62 x 10^⁵ 

E = hf= 6.63 x 10^^-34  x 4.62 x 10^⁵

 

= 3.06 x 10^^-33 J

 

Waves, Vibrations and Polarisation

Waves and Vibrations:

 

Waves that pass through a substance are vibrations that pass through the substance. Sound waves and seismic waves are examples of waves that pass through a substance and are often called mechanical waves. When waves progress through a substance, the particles of the substance vibrate in the same way. Electromagnetic waves are vibrating electric and magnetic fields that progress through space without the need for a substance. The vibrating electric field generates a vibrating magnetic field, which generates a vibrating electric field further away. Electromagnetic waves includes radio waves, visible light, ultraviolet radiation and many more (as shown in the diagram below)

 

 

Transverse waves: Waves in which the direction of vibration is perpendicular to the direction in which the wave travels. Examples: Electromagnetic waves and secondary seismic waves.

 

 

Longitudinal waves: Waves in which the direction of vibration of the particles is parallel to (along) the direction in which the wave travels. Examples: sound waves, primary seismic waves and compression waves.

Polarisation:



The process of transforming unpolarised light into polarised light is known as polarisation. It is possible to transform unpolarised light into polarised light. Polarised light waves are light waves in which the vibrations occur in a single plane.

 

Young's Modulus

Young's Modulus

When a stretching force (tensile force) is applied to an object, it will extend.  This is because the extension of an object is not only dependent on the material but also on other factors like dimensions of the object e.g. length etc. 

 

Stress is defined as the force per unit area of a material.
Stress = force / cross sectional area:

where,
σ = stress,
F = force applied, and
A= cross sectional area of the object.
Units of s : Nm^-2 or Pa.

Strain is defined as extension per unit length.
Strain = extension / original length

where,
ε = strain,
l_o = the original length
e = extension = (l-l_o), and
l = stretched length
Strain has no units because it is a ratio of lengths.


Stress is proportional to Strain. The gradient of a graph of stress against strain is Young's Modulus (E).

Therefore...

 

 

 

 

 

 

 

 

 

 

 

Units of the Young modulus E: Nm^-2 or Pa.

Alloys

An alloy is a mixture of two elements, one of which is a metal and contain atoms of different sizes.
 

 

It is more difficult for layers of atoms to slide over each other in alloys.

 

 

 

An example of an alloy is brass. Brass is made up of copper and zinc. It is mainly used in hinges and electrical plugs. Brass is also divided into many other brass alloys, but the most common type of brass contains 70% copper and 30% zinc. The density of brass is approximately 8.4g/cm3. If we take the volume of brass to be 160m3, then we can use the formula:

 

 

 

.. and rearrange the formula for mass. This would be: m = PV. Therefore, to find the mass of the copper and zinc contained in brass, we would need to find 70% of copper and 30% of zinc in brass and multiply both variables to find the mass of each metal.

 

Copper:

70% of 160m3 = 112m3

 

m = P x v

m = 8.4g/cm3 x 112m3

m = 940.8g

m1 = mass 1 = 940.8g

 

Zinc:

30% of 160m3 = 48m3

 

m = P x v

m = 8.4g/cm3 x 48m3

m = 403.2g

m2 = mass 2 = 403.2g

 

m1 + m2 = mT

940.8g + 403.2g = 1344g

 

 

 

 

 



Applying Hooke's Law to real life problems

When an elastic object - such as a spring - is stretched, the increased length is called its extension. The extension of an elastic object is directly proportional to the force applied to it
F = -kx

F   = Force (N)
-k  = Spring constant N/m
x   = Extension (m)

Hooke's Law can be explained using a small experiment I carried out at home. Force can also be calculated using the formula F=ma where (m) is mass and (a) is acceleration. A mattress contains springs inside and I wanted to find out the spring constant applied to the mattress.

Acceleration is calculated to be 9.81 m / s²  
I used my sister for this experiment. Her mass is 50kg.
Therefore F = 50 x 9.81 = 490.5 N

For the first formula, I have got the force and the extension, which is the depth of the mattress/length of springs. Therefore to find the spring constant, I will have to rearrange the formula to create the following:

k = F/x

Using the data I have got from the second formula, I now need to apply that to the first formula, which has been rearranged, to find the spring constant.

k = 490.5(N)/0.23(m)
   = 2132.608696 (N/m)
Therefore, a force of 2132.608696 (N/m) would be needed to extend the spring per 0.23m

Density used in real-life situations

A real life situation that uses density are ships and submarines. However, it can be hard to calculate whether an object would float on water. An object must contain a lot of air to float, therefore if the ship's density is less than the density of the water, the ship will be successful in floating. This is because ships store air in tanks which have a small density and have little mass. On the other hand, submarines are able to move around under water because their tanks of air are empty and have a higher density than water. Its overall density is greater than the surrounding water, and the submarine begins to sink. A submarine or a ship can float because the weight of water that it displaces is equal to the­ weight of the ship. This displacement of water creates an upward force called the buoyant force and acts opposite to gravity, which would pull the ship down.