PHYSICSSSS PART 3
So I've got another Physics exam tomorrow; here are my hardcore notes.
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Part 3: MUS
All sources of sound involve vibrations: a guitar string vibrates to produce sound. To create a vibration, every point in the string must oscillate with the same frequency.
An oscillation is a repeated cycle of motion performed by a single point or object. The oscillation can be represented in a displacement-time graph.
[[THERE SHOULD BE A FUCKING PICTURE HERE BUT LIVEJOURNAL IS TRYING TO MAKE ME PAY FOR PICTURES, THE BASTARDS]]
Amplitude is the maximum displacement from the original position, which is normally measured from the centre
The time period is the time it takes for one complete cycle
Frequency is the number of cycles per second, which is not always a whole number. It is measured in Hertz (Hz)
Frequency is the reciprocal of period, and vice versa - f = 1/T T = 1/f
Phase is the stage of a cycle of motion, given as a fraction of the cycle or as an angle. 1 cycle is 360 degrees, or 2pi radians.
TRAVELLING WAVES
Waves carry energy, beginning at an oscillation, and transport the energy from one place to another. They also carry information about the pattern of the original oscillation.
Wavelength - the distance between consectutive points in a phase - the distance between a phase difference of 2pi
Wavefront - The crest or trough that is the leading edge of a wave
Transverse wave - a wave that has displacements at right angles to the direction of travel of the wave - the classic wave shape.
Longitudinal wave - has displacements along the line of travel of the wave, which consists of compressions and rarefactions. This is like when you push along a spring, and parts of it are close together, and others are far apart.
Wave velocity:
The speed at which a wave travels determines how quickly energy can pass from place to place. You can't emit energy and have it recieved elsewhere at the very same time!
The wave advances by a distance of ONE WAVELENGTH in ONE TIME PERIOD, therefore velocity is wavelength divided by time period :
V = (lemda) / T = (lemda)f
SUPERPOSITION
When two sets of ripples overlap in a pond or two sets of sound waves arrive at the same time in your ear, they superpose.
Waves meet and combine to make one resultant wave, with the individual displacements added together.
Coherent waves have the same frequency and keep a constant phase relationship - they start and stop together.
In constructive superposition two waves re-enforce each other at a point where they always meet in phase.
In destructive superposition, the two waves meet out of phase and destroy one another partially (or completely if they have identical frequency and amplitude but are pi out of phase)
STANDING WAVES
Waves carry energy, but what if two waves carried equal amounts of energy in opposite directions along a wire, the energy would be confined between the fixed ends, and would produce a standing wave, because the waves would meet in phase and sometimes out of phase.
A standing wave consists of a pattern of nodes (minimum displacement) and antinodes (maximum displacement)
Musical notes are created by standing waves in a string or in air in the pipe which produce travelling waves in the surrounding airwith the same frequency. The simplest standing wave pattern give fundamental frequency, which has, in a string, nodes at either end and an antinode in the centre. The wavelength will be twice the length of the string.
In tubes, fundamental frequency is different. for a tube closed at one end, it will have a node at the closed end, and an antinode at the open end, and the wavelength will be FOUR TIMES the length of pipe. In a tube open at both ends it will have antinodes at both ends and a node in the centre, and the wavelength will be twice the length of the pipe.
Fundamental frequency is called f0, and the frequencies after that will be called f1, f2 etc., and each will have one more node and antinode than the previous.
Fundamental frequency is equal to 1 / 2L x the square root of T/ mu, where T is tension in newtons, and mu is kgm^-1
A musical note is formed by superposing many harmonic frequencies (multiples of f0) with the fundamental frequency itsself. This creates a complex repeating waveform in the fundamental frequency.
SOUND ANALYSIS
A specturum analyser produces a graph of amplitude against frequency for a selected sound waveform. The sound synthesiser superposes chosen frequencies to create a new wave form.
Non-musical sound is a mixture of frequencies which are not related in any simple way. Extreme mixtures that give no clear sense of overal frequency are called 'white noise'.
Noise is unwanted and/or meaningless sound. Acoustic engineers seek to enhance the desired sounds, while minimising any noise.
Active Noise Control is an example of 'two-souce superposition'. An antiphase signal superposes destructively with the ambient sounds. The two waves meet in antiphase and superpose, removing sound.
ANALOGUE AND DIGITAL
Older data storage systems, such a music stored on vinyl records and magnetic tape, are analogue systems. Newer systems are digital.
In analogue, the waveform varies continously and can take any value in a given range. Digital waveform varies in steps and takes discrete values only. Digital data is converted into Binary digits:
1011 = 11
1110 = 14
111010 = 58
The smooth/bumpy parts of a CD surface store the digital information, and they represent 0s and 1s. Superposition of the waves turns the light ON and OFF as it scans the disk.
On a smooth part of the disk the phase difference is zero, waves are reflected in phase so the output is 1.
In a bump of height a quarter of the wavelength, the path difference is half of a wavelength so the reflected waves are in antiphase and the output is 0.
REFLECTION AND REFRACTION
Waves transfer energy without carrying the material medium (if there is one) with them.
Angles of incidence and reflection will be equal about the normal when reflected, but when light is refracted (passes through an object and bends) their SINES will have a constant relationship with the REFRACTIVE INDEX of the material.
Refractive index a(mu)b = sin i/sin r = v1 / v2 = wavelength1 / wavelength 2
If you ever want to find out the refractive index of the first material, b(mu)a sin r/ sin i or 1 / a(mu)b
Convex lenses will converge light, to focus one parallel beam into a single bright spot. The distance from the lens to the focus point is called FOCAL LENGTH.
Critical angle (c) is the angle of incidence in the denser medium which makes the angle of refraction 90 degrees
Refractive index (mu) = 1 / sin c
Therefore ; c = sin^-1 (1 / mu)
POLARISED LIGHT
A wave is defined by having two motions; displacements (in the wave) and travel (of the wave)
Plane polarised light contains only one displacement direction.
Unpolarised light has a random mix of displacement in different directions.
Polarising filters absorb waves with particular displacement direction, but transmit waves wuth displacements at 90 degrees to this direction.
MODELLING LIGHT
Experiments so far show light carrying energy in a form of wave mtion, but to descrive how atoms emit and absorb this energy, we picture what lght is using a different model: it is made of of packets of energy called photons. The amount of energy in a photon is given by Planck's equation - E = hf
h = planck's constant, which is 6.63 x10^-34
Hot objects create continuous spectra with every frequency in a given range; electric currents in gases make line spectra with discrete frequencies.
Each atom in a gas discharge tube emits light independently of others, so the tube's spectrum is a result of energy exchange processes inside the individual atoms themselves.
Electrons inside a single atom have discrete energy levels. The neutral atom is the arrangement with lowest possible energy. When an atom gains energy (is excited), an electron moves to a higher energy level. When the energy is released, the electron moves to a lower energy level and radiation is emitted. The light frequency corresponds to the jump between the two levels.
The emissions will be in phase.
THIS IS THE END OF MUS. SPC coming next -dies-