|
Community Contributions - Articles by goIITians
|
|
|
| ~~~waves.....plzz see.......important.........!!!!!!!!!! |
|
|
Tagged with:
academic
|
![[Post New]](/templates/default/images/icon_minipost_new.gif) posted on 7 Oct 2007 23:18:39 IST
|
|
|
Oscillations, Vibrations and Waves
Simple Harmonic Motion Summary of Time relationships in SHM - Displacement is x = rsin(wt)
- Velocity is: v = wrcos(wt)
- Acceleration is: a = -w2rsin(wt) =-w2x
- Velocity is: v = +/- w?(r2- x2)
- Acceleration is: a = -w2x
Free osciallation describes a system in which the total energy of the system does not decrease with time A system which returns to its equilibrium position with no overshoot in the shortest possible time is said to critically damped
Wave Descriptions Transverse waves are defined as waves in which the displacements of the particles of the medium are perpendicular to the direction of wave travel. Can be polarised
Longitudinal waves are defined as waves in which the oscillation of the particles of the medium are parallel to the direction of wave travel. Cannot be polarised. Summary of terms associated with waves - The displacement of a particles is its instantaneous distance from the equilibrium.(s,x)
- The amplitude of a wave is defined as the maximum displacement of a particle from its equilibrium.(a,r)
- The wavelength of a wave is defined as the distance between any two points on adjacent cycles which are vibrating in phase.(?)
- The frequency of a wave is defined as the number of complete waves passing a given point per second.(f)
The velocity of the wave is given by: v = f lambda
Interference and Diffraction
The principle of superposition states: At a point where two or more waves meet, the instantaneous displacement is the vector sum of the individual displacements due to each wave at that point. This basically tells us that at the point where the waves meet, the resulting wave will depend not only on the amplitudes of each wave but also on their phase relationship.
Constructive intereference: for two sources in phase the path difference must be equal to an even number of half-wavelengths. Destructive intereference: for two sources in phase the path difference must be equal to an odd number of half-wavelengths.
Young's double-slit formula is: lambda = ws / D - where w = distance between adjacent fringes (fringe width).
- s = distance between slits (slit width).
- D = distance from slits to screen.
Diffration grating formula is dsintheta = nlambda - where d = grating spacing
- n = the spectrum order(i.e n = 1 for the first order diffraction image).
Stationary Waves Stationary waves are produced when two progressive waves of equal frequency and speed and nearly equal amplitude travelling in opposite direction are superimposed.
The velocity v of a transverse wave along a strecthed string is: v =  T / ? - where T = tension in the string
- = mass per unit length of string
Doppler Effect The Doppler effect for moving source(s) and moving listener(L) is: fL = (v + vL/ v + vs)*fs
- where v = velocity in medium -usually 340 m/s for sound
EM Spectrum | Wave Type | Wavelength Range(m) | Sources | Detectors |
|---|
| Radio | >0.001 | Oscillating charges | Antennae and tuned circuits |
|---|
| Microwave | 0.1-10-5 | Magnetrons and Klystrons | Antennae and tuned circuits |
|---|
| Infra-red | 10-4-7*10-7 | Thermal vibrations of atoms in hot bodies | Semiconductors, Photographic film |
|---|
| Visible | 7*10-7-4*10-7 | Energy level exchanges of electrons in atoms | Eye, Photographic film, Semidconductors |
|---|
| Ultra Violet | 4*10-7-10-9 | Energy level exchanges of electrons in atoms | Fluorescent chemicals, Photoelectric effect |
|---|
| X-rays | <5*10-8 | X ray tubes | Photographic film, Ionisation detectors |
|---|
| Gamma | <10-10 | Radioactive nuclei | Photographic film, Ionisation detectors |
|---|
Reflection and Refraction The law of refraction or sometimes known as Snell`s law is: n1sin?1 = n2sin?2
Examples of Refractive index values n | Medium | Symbol | Absolute Refractive Index |
|---|
| Air | na | 1.003 | | Water | nw | 1.33 | | Ice | ni | 1.30 | | Glass | ng | 1.50 | | Diamond | nd | 2.42 |
Total Internal Reflection occurs when light passing from one medium to another of lower refractive index is incident on the boundary at an angle greater than the critical angle for the two media. All of the light is reflected from the boundary, and there is no transmission.
The critical angle for Total Internal Reflection is: sin?crit = n1/n2 Lenses and Telescopes The Power of a lens is defined as P = 1 / focal length (f)
A Real image is one through which real rays of light actually pass and can therfore be formed on a screen. A Virtual image is one from which rays of light appear to have come and cannot be formed on a screen.
The lens formula for a thin lens is: 1/u + 1/v = 1/f - where u = object distance
- v = image distance
- f = focal length of lens
The linear magnification m is defined as: m = v / u
Resolving power-the angle of the first dark ring produced by a hole of diameter(w) with light of wavelength(?) is: sin? = 1.22 ? / w
|
About the Author:
|
this article: 2 points
(with 0 
in 1 votes ) [?]
|
|
You have to be logged on to rate
|
|
(posted on 8 Oct 2007 11:25:48 IST)
|
| good 1 there |
|
|
|
|
|
|
|
Back to Community Shelf
Awaiting Review for Nickels
1
