La Superposition Flashcards
State principle of superposition
when 2 or more waves meet at pt, resultant displacement at that pt equals vector sum of displacements of individual waves at that pt
Define interference
phenomenon occurring when 2 or more waves of same type superpose according to principle of superpos n
What are 2 types of interference? When do they occur?
- Constructive (regions of max energy)
occurs whenever 2 waves meet IN PHASE, superpose to produce resultant w max amplitude, intensity - Destructive (regions of min energy)
occurs whenever 2 waves meet 180° OUT OF PHASE/ANTIPHASE, superpose to produce resultant w min amplitude, intensity (need not be 0)
What 2 factors affect phase diff btw 2 waves?
- diff btw distance travelled by 2 waves fr sources to that pt (path diff)
- phase diff btw sources
What interference is formed for sources that are in 1. phase and in 2. antiphase for path diff of nλ and (n+0.5)λ respectively? (λ is any +ve integer)
- Source in phase
- nλ : constructive
- (n+0.5)λ : destructive - Source in antiphase
- nλ : destructive
- (n+0.5)λ : constructive
What are 3 conditions needed for steady & observable interference patterns? Explain why for each
- Overlapping waves must b coherent
(waves r coherent if they hv constant phase diff/ r/s btw them & same f)
so that a constant interference pattern can be obtained. - Waves shd hv equal, similar amplitudes
so that complete or almost complete cancellation is achieved at points of destructive interference. (and there will be good contrast btw maxima & minima) - Transverse waves must b either polarised in same plane or unpolarised
If not polarised in the same plane, then complete cancellation is not possible even at points where the two waves are completely out of phase.
Define diffraction
spreading of waves after passing thru small opening or around an obstacle
When does diffraction appear most significant?
When size of aperture/obstacle is of same order of magnitude as wavelength of wave
What is the double slit formula. When is it valid?
x=λD/a
where
x is fringe separation (dist btw successive bright fringes),
λ is light’s wavelength,
D is dist fr double slits to screen
a is separat n of two slits (measure fr centre to centre of slits)
-oni valid when D is much larger than a (usually ~100 times bigger)
What is the single-slit formula to find minima? What also to take note of?
sinθ= λ/b
(also note that:)
tanθ=d/D and for small θ, sinθ ≈ tanθ
where
d is dist from broad central maximum to first minima,
D is distance from slit to screen,
θ is angle at which first minima occurs (btw, D and line fr middle of slit to first minima)
λ is light’s wavelength,
b is width of single slit
Define Rayleigh’s Criterion. What is the formula?
When central maximum of 1 image falls on 1st minimum of another image, the images are distinguishable & said to be just resolved. This limiting condit n of resolut n is known as Rayleigh’s criterion
θmin = λ/b
where
θmin is limiting angle of resolut n,
λ is light’s wavelength,
b is width of single slit
What is the diffraction grating formula? What is the condition?
dsinθ = nλ
where
d is line spacing (slit separation) of diffraction taking (calculated by 1/N, N is no of lines per m or mm),
θ is angle btw nth order beam & normal to grating,
n is order of diffraction, an integer (n=0,1,2,3…),
λ is incident beam’s wavelength
For fringe to b observable, θ<90°
Define formation of stationary waves
stationary wave is result of interference:
- btw 2 identical waves (same type) of same amplitude, f & v;
- travelling along same line in opp direct n, & overlap
What is the difference btw stationary (S) and progressive (P) wave?
- Wave profile:
- S: vary fr one extreme pos n to another, does not advance
- P: advance w speed of wave - Energy of wave:
- S: energy retained within vibratory motion of wave
- P: energy transferred in direct n of wave propagat n - Amplitude of oscillat n of indivi particles
- S: depends on pos n along wave; particles at antinodes oscillate w max amplitude; particles at nodes do not oscillate
- P: same for all particles in wave regardless of pos n (assuming no energy loss) - wavelength
- S: twice distance btw 2 adjacent nodes/antinodes; equal to wavelength of component waves
- P: distance btw any 2 consecutive pt on wave w same phase - phase of wave particles in a wave length
- S: all particles btw 2 adjacent nodes in phase; particles in alternate segments in antiphase
- P: wave particles hv diff phases (0 to 2π) within wavelength
What is the harmonic series, overtone, mode of vibrat n, wavelength and f of 2 fixed ends of stretched string?
*as ends of wave are fixed, nodes occur at both ends
(let n be an +ve integer starting from 1, L be length btw 2 ends of string, v be speed)
- harmonic series: n
- overtone: n-1
- mode of vibrat n: all harmonics possible
- wavelength = 2L/n
- f = nv/(2L)
