Nature of science: Oscillations in nature
- Oscillations is basically everywhere and Is very common in our daily lives without us realizing it.
- Hummingbird flaps its wring at frequency of 20 beats per second.
- Electrocardiographs are used to monitor heartbeats
- Stroboscopes to freeze motion in engines and motors.
- Practical techniques have been developed with mathematical modeling that is used to interpret oscillations are very powerful tools. It can help human by understand and making predictions about natural phenomenon.
- Isochronous: taking the same time.
- Definition: Oscillations that are repeated in the same time period.
Describing periodic motion
- As the mass passes its rest or equilibrium position its displacement (s) is zero.
- Amplitude: Maximum value of the displacement
- Frequency of an oscillation: is the number of oscillations completed per unit time.
- Frequency: is the number of oscillations per second
- Period: the time for one oscillation
Simple harmonic motion
To perform SHM It requires an object to have restoring force acting on it.
- Magnitude of force is proportional to the displacement of the body
- Direction of the force is always towards the fixed point
Fixed point is the equilibrium position of the mass.
4.2 Travelling waves
Two fundamental types of waves: Mechanical waves and Electromagnetic waves
- Mechanical – requires material medium to travel
- Electromagnetic – able to travel through vacuum
- λ is shortest distance between two points that are in phase on awave
- f is number of vibrations per second performed by the seource of the waves and so is equivalent to the number of crest passing a fixed point per second.
- T is the time that it takes for one complete wavelength to pass a fixed point or for a particle to do complete oscillation.
- A is maximum displacement of a wave from its rest position.
- particles are more bunched up than normal
- particles are more spread out than normal
Displacement Time Graph
- describes displacement of one particle at a certain position during a continous range of time.
- wave velocity given by
- c = f λ
- Electromagnetic waves that can pass through layers of atmosphere.
- All electromagnetic waves (except gamma rays) produced when electrons undergo an energy change even though the mechanisms might be different.
- They are transverse, carry energy, and exhibit full range of wave properties
- Produced when electrons undergo energy change
4.3 Wave characteristics
- surface that travels with a wave and is perpendicular to the direction in which the wave travels (the ray).
- line showing the direction in which a wave transfers energy and is perpendicular to the wavefront.
Principle of superposition
- When two or more waves meet the total displacement is the vector sum of their individual displacements.
- Polarization of a transverse wave restricts the direction of oscillations to a plane perpendicular to the direction of propagation.
- Electromagnetic waves – unpolarized
- Direction of vibration stays constant over time
- When there is some restriction to direction of vibration but not 100%.
- When totally plane-polarized light (from a polarizer) is incident on an analyser, the intensity of the light transmitted by the analyser is directly proportional to the square of the cosine of angle between the transmission axes to the analyser and polarizer.
4.4 Wave behavior
Laws of reflection and refraction;
- Reflected and refracted rays are in the same plane as the incident ray and the normal
- Event of reflection or refraction does not alter the pane in which the light ray travels
- The angle of incidence equals the angle of reflection
- Angle of incidence is the angle between the incident ray and the normal and the angle of reflection is the angle between the reflected ray and the normal.
- For waves of a particular frequency and for a chosen pair of media the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant called the (relative) refractive index
- Snell’s Law (or Descartes’ law) – The angle of refraction is the angle between the refracted and the normal
Absolute refracted index
- Speed of electromagnetic waves in vacuum / speed of electromagnetic waves in medium
- Rays are reversible
- is an angle of incidence when the angle of refraction is 90 degree.
Total internal reflection
- angle of incidence is larger than the critical angle.
- when path of wave is partly blocked by an object, it spreads out.
Double slit interference
- Two waves or more meet and combine to produce a new wave.
- When resultant wave has larger amplitude than any of the individual waves and the interference is constructive.
- when the resultant has smaller amplitude and so the interference is destructive.
4.5 Standing waves
- Waves can be formed in which the positions of the crests and trough do not change
Standing waves formed when
- two travelling waves of equal amplitude and equal frequency traveling with the same speed in opposite direction are superposed
Standing waves on string
- total displacement always remain zero
- displacement varies between a maximum in one direction and a max in other direction
- A string is strung between a vibration generator and a fixed end to demonstrate waves.
Harmonics on strings
- There are a number of frequencies that naturally vibrate.
- Those natural frequencies are called harmonic of strings.
Harmonics on pipe
- A harmonic is named by the ratio of the frequency and to that first harmonic.
- Fixed boundary – the wave reflects (or at least partially reflects)
- Free boundary – the reflected wave does not cancel the incident wave and there is an antinode formed