SUPERPOSITION
when >1 wave w/ same freq overlap => interference (illustrated by ripple tank)

2 sources A & B w/ equal freq giving circular waves
principle of superposition can explain interference pattern
along RS: A_crest and B_crest meet at same time > constructive interference > large wave along RS
along XY: A_crest and B_trough meet at same time > destructive interference > no wave along XY(> every pt on XY:

/2 nearer to A)
reinforcement: constructive interference- at pt C when path diff AC - BC = k

Z⁺)
cancellation: destructive interference- at pt C when path diff AC - BC = (k+½)

Z⁺)

Principle of superposition:
when 2 waves travel through, the resultant displacement at any pt = vector sum of separate displacement due to the 2 waves

Interference of microwaves

max & min detected along AB due to inter. of wave from PQ
Interference of sound waves

2 loudspeakers in // w/ audio freq oscillator microphone/ ear moved along MN: alternate loud & soft

Conditions for 2-source interference
-coherent sources: same freq (=> same

), in phase/ w/ const phase diff
-~ same amplitude (or else no min)
-for transverse waves: -unpolarised / -polarised in same plane
-for light: sources v.clost as

of light is v.small (not close: light & dark bands v.close => can't be seen)

Young's double slit experiment

A, B, C: narrow slits, A & B: v. close together
bright & dark bands seen on both sides of O (perpendicular bisector of AB)
[width of slits = 0.2mm, separation of double slit = 0.5mm]
white light used: diff colours > diff

P = m^th bright line, BP - AP = m

PA = PN = > BN = BP - AP = m

AB is v.small > PM >> AB => AN & PN meet at ~90° =>

PMO

BAN =

BAN: sin

= BN/AB = m

PMO: tan

= PO/MO = x_m/D

is v.small, tan

sin

=> x_m/D = m

/a => x_m = mD

/a
Q: neighborring bright fringe- OQ = x_m-1 = (m-1)D

fringe separation, x = D

/a [D: separation of double slit & screen, a: separation of double slit,

: wavelength of wave]

_light: 10^-6m
source slit closer to double slit: x unaffected (only brighter)
source slit widened & widened > fringes gradually disappear (large slit acts as several narrow slits > many interference patterns at diff places > dark & bright fringes overlap > uniform illumination)
white light used: central fringe = white, other fringes = colour
blue fringe (smallest

) closest to central, red fringe (largest

) furthest from central

Diffraction = spreading of wave when wave pass through aperture / around obstacles

generally: smaller aperture (compared to

) > more diffraction

_light= 6 × 10^-7m => small objects/ aperture: sig diffraction of light

sound waves can diffract around wide openings as opening comparable to _sound
diff ∝

(low notes heard easier than high notes)

Single slit diffraction

A & B: on plane wavefront & can be considered as 2 secondary sources of light, since from same wavefront => coherent w/ identical amplitude =>interference pattern as long as slit is narrow (rel to

)
short dist beyond M & N (projections of A & B): alternate bright & dark fringes
central fridge: twice as wide as & intensity v.much greater than other bright fringes
sin

/d (d: separation of double slit)

Increasing # of slits

each slit: similar diffraction effect in same direction > pattern similar to 1 slit w/ intensity variation (but crossed by intermediate fringes due to interference bet slits)
more // equidistant slits; intensity & sharpness of: -principal max increases, -subsidary max decreases
100's slits/mm: only a few sharp principal maxima

diffraction grating: glass/ metal w/ large # of close // equidistant slits ruled on it

grating w/ n lines/mm: d = 1/(n × 10⁴)m
BC = dsin

= path diff bet 2 adjacent slits
for bright fringe: BC = k

(k = whole #/0)
=> sin

= BC/AB = k /d => dsin

= k

1st order bright fringe = 1st adjacent fringe to central fringe

more slits > less # of bright fringes which are brighter

Measurement of wavelength

find 1st order of diffraction on each side => angular diff = 2

= dsin

(k = 1)

Stationary /standing waves
-formed when 2 identical waves (same freq + amp) travel in opp directions in a medium
-wave-like profile doesn't move along medium

N-nodes = pts of permanent zero displacement
A-anti-nodes = pts ½ way bet 2 nodes w/ max amplitude of vibration (vib: 0

2 amp._original)
dist bet 2 nodes, NN =

/2, AA =

/2, AN =

/4

Modes of vibrations of stretched string

fundamental freq, f₀ (1^st harmonic): l =

/2 => f₀ = v/

= v/2l

1^st overtone, f₁ (2^nd harmonic): l =

₁ => f₀ = v/

₁ = v/l = 2f₀

2^nd overtone, f₂ (3^rd harmonic): l =3

₁/2 => f₀ = v/

₂ = 3v/2l = 3f₀

nth overtone: (n+1)f₀
Stationary waves in air columns
closed pipe- open end always anti-node, closed end = node
open pipe- both ends always anti-node

	closed	open
fundamental freq, f₀ (1^st harmonic)	l =/4 => f₀ = v/ = v/4l	l =/2 => f₀ = v/ = v/2l
1^st overtone, f₁ (2^nd harmonic)	l =3₁/4 => f₁ = v/₁ = 3v/4l = 3f₀	l =₁ => f₁ = v/₁ = v/l = 2f₀
2^nd overtone, f₂ (3^rd harmonic)	l =5₂/4 => f₂ = v/₂ = 5v/4l = 5f₀	l =3₂/2 => f₂ = v/₂ = 3v/2l = 3f₀
nth overtone	(2n+1)f₀	(n+1)f₀

Measuring of sound using stationary waves

sound waves of const freq emitted from loudspeaker aimed at reflecting surface > sound reflected > interfere w/ incident waves > stationary waves set up
microphone, connected to y-plates of oscilloscope, moved through region of standing waves
mic placed at 2 successive max pts (anti-nodes- loudest sound) => dist, x, bet pts =

/2 =>

= 2x
anti-node >(move)> node: loud > soft sound, node >(move)> anti -node: soft > loud sound

Calculate velocity of sound in air by Kurdt's tube

freq of sound varied, resonance occurs when f equals natural freq of vib of air column in tube > stationary waves formed > lycopdium powder collects in heaps at nodes (no disturbance)
av. dist bet 2 heaps/nodes =

/2

Resonance tube experiments

A: anti-node actually slightly above rim, dist 'c' above rim
at 1^st resonance: l₁ + c =

/4
at 2^nd resonance: l₂ + c = 3

/4
l₂ - l₁ =

/2

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