P4: Properties of Waves

General wave properties

Waves transfer energy without transferring matter
They are illustrated by wavefronts, which each represent different waves from above
Wave equation: Velocity (m/s) = Frequency (Hz) x Wavelength (m) OR (v = f x λ)

Waves have many different features. These include...

Speed: The speed of the wave is simply how fast it travels. It is worked out by Wavelength x Frequency. Its unit is meters per second (m/s)
Frequency: The frequency of the wave is a measure of the number of complete waves that passes a point in a second. Its unit is hertz (Hz)
Wavelength: The wavelength is the distance between two of the same points in consecutive waves. Its unit is meters (m)
Amplitude: The amplitude of a wave is the height of the wave. It is the difference between the height of the crest (highest point in the wave) and the height of the trough (lowest point in the wave)

Transverse and Longitudinal Waves

There are two main types of waves: transverse and longitudinal
Transverse waves are waves that have points that vibrate perpendicular to the direction of the energy transfer
Longitudinal waves are waves that have points that vibrate in the same direction as the direction of the energy transfer

Longitudinal and transverse waves

Reflection, Refraction, and Diffraction

Reflection

Reflection happens when a wave touches a surface
The angle of incidence (the angle at which the wave touches the surface) and the angle of refraction (the angle at which the wave is reflected) are always the same

Image of reflection

Refraction

When waves enter a different medium, the speed it travels at changes
This changes the direction and the wavelength of the wave
If waves become slower, the wavelength will decrease
If waves become faster, the wavelength will increase

Diffraction

When waves go through a narrow gap or pass an edge, they spread out
This happens when the wavelength of the wave is smaller than the gap
There is more diffraction with a smaller gap

Image of diffraction

Light

Light is a transverse wave on the electromagnetic spectrum

Reflection of Light

A useful application for the reflection of light is on mirrors
Light waves creating images which can be reflected on a mirror
The image will be of the same size as the object, same distance from the mirror as the object, and will be directly in front of it as well
The angle of incidence is equal to the angle of reflection
An image is created because

As the angle of incidence is equal to the angle of reflection, the observer would think that the image comes from where the reflected ray came from
As objects reflect light, the many light rays will reflect on the mirror
By extending the reflected rays into the direction of the mirror, the reflected rays will eventually meet a point
That point is where the image forms
The image shown on a mirror is called the virtual images, and the extension of the reflected rays are called virtual rays

Diagram of reflection of light

Refraction of Light

When light enters a different material, the speed of light changes, causing it to refract and travel in a different direction
An investigation that shows the refraction of light is done through refracting light on a glass block, and helps us find the refraction index of the material the light ray passes through
Here are the steps of the investigation

Place a glass block on top of a piece of paper, and draw the outline of the block on the paper
Using a ray box, create a light ray that passes through the glass block
Mark the following points to draw the direction of the light rays on paper

A point where the light ray has yet to touch the box
The point the light ray enters the box
The point where the light ray leaves the box
A point after the light ray has left the box

Remove the block and connect the points to form straight lines which show the direction of the light rays
Do this for several light rays to work out the refractive index

All materials have a refractive index which indicates the ratio of the speed light travels in the material to the speed light travels in a vacuum
The refractive index is worked out by the equation: Refractive index= sin(angle of incidence)/sin(angle of refraction) OR n = sin i / sin r
The angle of incidence is the angle which the light ray hits the material
The angle of refraction is the angle which the light ray refracts within the material
When a light ray enters a material with a higher refractive index, the light ray will travel towards the normal

Diagram of refraction of light

Materials also have a critical angle, which is the angle of incidence where the angle of refraction is 90°. Any angle higher would cause light rays to reflect within the material instead
The critical angle can be found by the refractive index with this equation: sin(critical angle) = 1/refractive index
When all these light rays are reflected it is called total internal reflection
This concept is used in optical fibres, which allows data to travel back and forth quickly on the internet
Optical fibres can also be used for medicine to see within the human body (with the light reflected within the optical fibres)

Thin converging lens

A converging lens is a lens that allows rays of light parallel to the principle axis, the center of the lens) to focus onto a principle focus point
The curve of the lens determines how far the principle focus point is away from it. This distance is called the focal length
Lenses form real images of objects in front of them
The position of the the image can be determined by drawing a ray diagram

The method to draw a ray diagram is as follows

First, draw a line from the top of the object parallel to the principle axis to where it touches the lens above the center
When it has reached the middle of the lens, draw a line connecting it from the end of the previous line so that it passes the principle point
Finally, draw another line from the top of the object through the center of the lens so that it touches the previous line. The point where the lines intersect is where the image will form

The image formed will always be a real and inverted image

Depending on the distance of the object from the lens, the image is either enlargened, diminished, or the same size

If the object is placed at a distance further than 2 times the focal length away from the lens, then the image will be diminished (becomes smaller than the object)
If the object is placed at a distance less than 2 times the focal length away from the lens, then the image will be enlargened (becomes larger than the object)
If the object is placed at a distance of 2 times the focal length away from the lens, the iamge will be the same size as the image

Differences between a real image and virtual image

A real image is formed by the convergence (meeting) of many light rays
Real images can be projected on a screen
Virtual images are formed by refraction or reflection
Virtual images cannot be projected on a screen

Use of the single lens in a magnifying glass

When an object is at a distance from the length closer to the focal length, the rays diverge and do not form a real image as the rays do not converge
However, a virtual image is formed from light rays from the object that through the glass. The image will be enlargened

Electromagnetic Spectrum

The electromagnetic spectrum is a range of waves that have different frequencies and energies

These waves are all transverse
They all can travel in a vacuum
They all travel at the same speed in a vacuum (of 3.0 × 10⁸m/s) and similar speeds in air
Different radiomagnetic waves have different uses

Radio waves: Used for wireless communication, as they can transmit easily in the air and do not harm the human body as much due to its lower frequency
Micro waves: Used for wireless communication (WiFi, radar, mobile phones, satellite communciations), and heating things at a high intensity (eg. in a microwave)
Infrared rays: Used in surveillance cameras to see in the dark, send signals to TVs in remotes, and are used in optic cables. They are also used in more purposes in industry, medicine, and research
Visible light: Used to see and take photos and videos
Ultraviolet rays: Ultraviolent is absorbed in some substances and make them emit visible light, which makes this used in fluorescent light bulbs and secret marks using an invisible ink that can be seen through flashing a light on it
X-rays: Used in medicines to pass through body tissues and be absorbed by bones, creating an image that show the bones within the body
Gamma rays: Used to kill cells and living tissue, and is very dangerous due to its high frequency. It is also used for killing off bacteria

Dangers of electromagnetic rays

Microwaves: In an excessive amount, they can cause your organs to heat up
X-Rays: Can cause harm to body tissue because of its high frequency, which is why there is a lead vest and an attempt to minimise the exposure of patients to X-rays
Ultraviolet Rays: Ultraviolet radiation can cause health risks such as skin cancer, skin damage, cataracts or eye damage, and immune system suppression when an individual is exposed to ultraviolet rays too much. These ultraviolet rays often come from the Sun or tanning lamps

Sound

Sound (longitudinal) waves are produced by vibrating particles
Sound cannot travel through a vacuum (such as in space) and need to travel through a medium as sound is spread through vibrations
Sound waves with a greater amplitude create a larger sound, and waves with a smaller amplitude create a softer sound
Sound waves with a great frequency create sounds at a higher pitch, and waves with a smaller frequency create sounds at a softer pitch
Sound waves can be reflected and create echoes
Sound waves consist of compressions (where particles are more concentrated and packed together) and rarefactions (are less concentrated and further apart)
A healthy human can hear sound waves with frequencies 20Hz-20,000Hz
Sound travels faster in solids than in liquids as the moleecules are closer together and can transmit vibrations better
The formula to find the speed of a wave is v = λ x f

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