The Nature of Waves
The nature of Waves
Waves usually carry energy and information from one place to another
The wavelength is the distance from peak to peak
The amplitude of a wave is how high the peak gets
Frequency is the number of vibrations per second passing a given point
Period is the time taken for one whole vibration
Frequency = 1 / period
Speed of wave (v or c) = wavelength (λ) * frequency (ƒ)
Reflection and Refraction
Reflection and Refraction
Reflection- the wave is bounced back when it hits something e.g a mirror
Refraction- the wave changes direction as it enters a different medium. Diffraction happens because a wave slows down or speeds up
Key words= yellow
Transverse waves and polarisation
Transverse waves and polarisation
All electromagnetic waves are transverse waves
They can be drawn as displacement against distance or displacement against time
Not all waves are transverse, sound waves are longditudinal
A polarised wave only travels in one direction
Electromagnetic radiation is made up of two transverse waves
A polarisation filter acts like a block for a transverse waves. Light that has passed through a polarisation filter will only be vibrating in one direction
When light reflects it is partially polarised
Forming images with with lenses
Converging lenses change the curvature of the wavefronts by refraction
The focal point, f, is the distance between the lens axsis and the focus
the more powerfull (thicker) a lens is the more strongly it will curve the wavefronts
curvature = 1 / radius of the curvature or power = 1/f
This is the lens equation
V= distance between image and the lens axis
U=distance between the object and the lens axis
Diagram of forming images
this is a diagram of how it works
A lens can also produce magnification
to work out linear magnification use this formula
magnification= size of image (v) / size of object (u)
Information in images
The binary system, like the decimal sysrem is a way of writing numbers.
it uses 0 and 1
e.g 0=0, 1=1 , 10= 2 , 11= 3
a single binary digit is called a bit while a group of eight is called a byte
Data is saved onto a computers memory using the binary system
It is saved as a string of bits.
The number of bits in a string determines the number of possabilities e.g 1 bit has 1 two alternative while a byte has 256 alternatives
Number of alternatives = 2 to the power of number of bits
Number of bits = log2 number of alternatives
Information in images (continued)
Images are stored as arrays of binary numbers
If you zoom into a digital photograph you can see the induvidul pixels
Each pixel is represented by a binary number
the value of a binary number gives the colour of the pixel, e.g if an image is made up of 256 shades of gray then each pixel is represented by an eight digit binary number
In coloured images each pixel can be described by three binary numbers, each of them the primary colours of light (red, green and blue) , the length of a binary number depends how many different colours are used.
Multiplying by a fixed value improves contrast
multiplying by a fixed value greater than one makes the image brighter and increases the contrast
adding by a fixed value only makes the image brighter it does not increase the contrast
Adding false colour highlights features
Changing induvidual values to different colours makes certain features of the image stand out
Replacing pixels with median of their neighbour reduces noise
Noise is unwanted interference, in images it is usually a bright or dark spot. This method smoothes the image
The laplace rule is used to find edges just multiply by 4 and then subtract the pixel values from above, below, left and right. The result is that any pixel not on an edge goes black
Analogue and digital signals
Digital signals are represented by binary numbers. The values that a digital signal can take depend on the number of bits used e.g one bit signal can only take the values 0 and 1, but a one byte signal can take 256 different values.
Analogue signals are not limited in the values they can take- they vary continously over a range of loudness and frequency.
Digital signals are resistant to the effects of noise. Analogue signals pick up noise interference from electrical disturbances or other signals. The reciever needs to be able to reconstruct the original signal if they're to get and acurate representation of what was sent. This is much easier with a digital signal than an analogue because the number of values a digital signal can take is limited.
Analogue signals can be digitised , to do this you take the value of the signal at regular time intervals, then find the nearest digital value. Each digital value is represented by a binary number so you can convert the analogue values to binary numbers. The digital signal you end up with will not be the exact value but it is usually quite close.
The quality of the digitised signal depends on its resolution and the sampling rate. The greater the number of bits the greater the sampling rate
Noise limits the number of bits used for sampling as you might end up reproducing all the the noise from the signal.
Maximium number of bits =log 2 (total variation/ noise variation)
If the sampling rate is low it will create aliases that were not in the original signal at all
Minimum sampling rate = 2 x maximum frequency of the signal
Advantages of digital signals
They are easier to send and recieve because they can only take a limited number of values. They are ressistant to the effects of noise. They can be used to represent differents types of info. They are easy to process on a computer.
signal spectra and bandwidth
signals are made up of lots of different frequencies. Frequencies that make up a signal are called a spectrum.
If you want to reconstruct a signal you need to know about all the frequencies in within it. This is why the sampling rate is so important when digitising signals.
You can get information about frequencies within a signal by drawing a graph of it's spectrum.
The bandwidth is the range of frequencies within a signal. In communication systems the bandwith determines how many signals can be sent at the same time.
Bandwidth = highest frequency - lowest frequency
Communication signals are transmitted using carrier waves
Rate of transmission (bits per second) = sample per second x bits per sample