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### Transcript of class 38 Properties of waves - Mr. Gopie...

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PHYSICS  WAVES

Mr  Rishi  Gopie

• Mr  R  Gopie   PHYSICS

Page  2  of  14

Properties  of  waves

a) Reflection  (at  a  plane  boundary)  –  after  which  f,  λ  and  speed  (v)  remain  the  same.  consider:

i) Plane  wavefronts

Diag.  9

• Mr  R  Gopie   PHYSICS

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ii) Circular  wavefronts

Diag.  10

• Mr  R  Gopie   PHYSICS

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b) Refraction  (at  a  plane  boundary)

Diag.  11

Note  the  following:

i) λ1  >  λ2

ii) f  remains  constant

iii) v1  >    v2

iv) n  =  λ1/λ2      =  v1/  v2    =  sin  i/  sin  r

v) for  water  waves

• Mr  R  Gopie   PHYSICS

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diag.  12

vi) Generally,  for  any  type  of  wave  (such  as  water  waves,  light  waves,  sound  waves  etc.):

1) wavelength  is  greater  in  the  less  dense  medium

2) speed  is  greater  in  the  less  dense  medium

3) frequency  remains  the  same

4) refraction  occurs  towards  the  normal  in  the  denser  medium  and  away  from  the

normal  in  the  less  dense  medium

5) for  the  denser  medium:

n  =  wavelength  (speed)  of  the  waves  in  the  less  dense  medium/wavelength  (speed)

of  the  waves  in  the  denser  medium

6) Refraction  occurs  when  a  wave  passes  from  one  medium  into  another  in  which  it

has  a  different  speed  and  wavelength  and  the  angle  of  incidence  at  the  boundary

between  the  media  is  not  zero.

• Mr  R  Gopie   PHYSICS

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c) Diffraction

This  is  the  spreading  of  waves  as  they  pass  through  an  opening  or  aperture  such  as  a  gap  or

a  slit  (and  as  they  pass  around  the  edge  of  an  obstacle)  the  width  a.  Of  which  is  comparable

with  the  wavelength  (λ)  of  the  waves.

• Mr  R  Gopie   PHYSICS

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• Mr  R  Gopie   PHYSICS

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Diag.  13

In  all  cases,  for  the  emerging  waves:  f,  λ  and  speed  (v)  remain  the  same  as  for  the  incident  rays.

For  a  given  width  of  opening/aperture/gap/slit  (i.e.  for  a  fixed  a):  increasing  λ  of  the  incident  waves

increases  the  amount  of  diffraction,  i.e.  spreading  of  the  waves  (e.g.  red  light  is  diffracted  more  than

blue  light  ,  by  the  same  opening,  since  λa  >  λb  )

For  a  given  wavelength  of  incident  waves  (i.e.  a  fixed  λ):  decreasing  a  increases  the  amount  of

diffraction  waves.

Since  the  wavelength  of  visible  light  are  very  small  then  the  diffraction  of  light  in  ordinary

circumstances  is  not  observed  –  instead,  light  appears  to  travel  in  straight  lines  rather  than  to  be

diffracted.  However,  the  wavelengths  of  the  sound  waves  and  water  waves  are  usually  much  larger

than  those  for  visible  light  and  so  their  diffraction  effects  are  much  more  common  and  easier  to

observe  –  for  instance,  sound  can  be  heard  round  obstacles,  such  as  doorways,  while  the  source  of

the  sound  cannot  be  seen  around  the  same  obstacles.  Also,  water  waves  are  observed  to  spread

through/around  openings  in  ripple  tanks  (and  in  bays  on  coastlines).

June  2000  p2  q2

• Mr  R  Gopie   PHYSICS

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d) Interference

The  principle  of  superposition  states  that  when  two(or  more)  waves  meet  at  the  same  point

in  space  the  resultant  displacement  at  that  point  is  the  vector  sum  of  the  individual

displacements  that  each  of  the  waves  would  produce,  by  itself,  at  that  point  in  space.

Coherent  sources  of  waves  are  sources  which  produce  waves  that  have  a  constant  phase

difference  between  them.  Such  waves  are  said  to  be,  themselves,  coherent.  They  also  have

the  same  wavelength,  frequency  and  speed.

Interference  between  waves  is  produced  where  two  (or  more)  coherent  waves  meet.  The

waves  undergo  superposition  and  produce  a  pattern  of  resultant  waves.  This  effect  is

known  as  interference.  Where  the  waves  meet  and  undergo  superposition  in  phase  (i.e.  with

crest  –  on  –  crest  and  trough  –  on  –  trough)  then  constructive  interference  occurs  and  the

amplitude  of  the  resultant  wave  is  the  sum  of  the  amplitudes  of  the  two  interfering  waves.  A

maximum  of  intensity  is  thus  obtained.

Where  waves  meet  and  undergo  superposition  exactly  out-‐of-‐phase,  i.e.  180°  out-‐of-‐phase

or  in  antiphase  (with  crest-‐on-‐trough  and  trough-‐on-‐crest)  then  destructive  interference

occurs  and  the  amplitude  of  the  resultant  wave  is  the  difference  between  the  amplitudes  of

the  two  interfering  waves.  A  minimum  of  intensity  is  thus  obtained

Consider  the  following:

• Mr  R  Gopie   PHYSICS

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Diag.  14

In  a  case  of  such  interference  the  resultant  wave  (if  there  is  one)  has  the  same  λ,  f  and  speed

(v)  as  the  interfering  coherent  wave.

• Mr  R  Gopie   PHYSICS

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Consider  the  physical  meaning  of  interference  for  various  waves:

Examples  of  Waves   Effects  Produced  for:

Constructive  Interference   Destructive  Interference

Water  Waves   High  Crests  and  lower  troughs   Lower  crests  and  higher

troughs  (or  a  flat  surface  for

interfering  coherent  waves  of

the  same  amplitude)

Light  Waves   Brighter  Light   Dimmer  light  (or  darkness  for

interfering  coherent  waves  of

the  same  amplitude.

Sound  Waves   Louder  Sounds   Softer  sound  (or  silence  from

interfering  coherent  waves  of

the  same  amplitude.

All  waves  (and  only  waves  –  not  particles  )  can  undergo  diffraction  and  interference  where

waves  from  2  (two)  coherent  sources  overlap,  interference  patterns  are  produced  in  the

region  of  overlap.

• Mr  R  Gopie   PHYSICS

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Diag.  15

It  is  impossible  to  obtain  two  independent  sources  of  light  waves  that  are  coherent,  so  a

single  source  must  be  divided  into  two  secondary  sources  (such  as  a  pair  of  slits  i.e.  double

slit).  Since  these  two  secondary  sources  come  from  the  same  primary  source  then  the  waves

they  produce  must  be  coherent.  Young`s  double  slit  experiment  investigates  an  interference

pattern  for  light  waves.  Consider  a  typical  arrangement.

• Mr  R  Gopie   PHYSICS

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Diag.  16

The  interference  pattern  is  produced  on  a  screen  as  a  fringe  pattern,  i.e.  a  series  of

alternating  bright  (B)  and  dark  (D)  fringes  or  bands.  The  centre  of  a  bright  fringe

corresponds  to  a  region  of  constructive  interference  and  the  centre  of  a  dark  fringe

corresponds  to  a  region  of  destructive  interference.

The  equation  that  applies  in  this  situation  is  :  𝑥 =  𝜆𝐷/𝑑

Where  x  is  the  fringe  separation  (i.e.  the  distance  between  the  centres  of  adjacent  bright

fringes/bands).

D  is  the  distance  between  the  double  slit  arrangement  and  the  screen,  d  is  the  slit  separation

(i.e.  the  distance  between  the  centres  of  the  two  slits),  λ  is  the  wavelength  of  the  wave.

Once  d  and  D  are  constant  then𝑥   ∝  𝜆,  i.e.  the  fringes  get  closer  together  as  the  wavelength

of  light  decreases  (for  instance  as  the  colour  of  the  light  changes  from  red  to  blue).

• Mr  R  Gopie   PHYSICS

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Also,  once  λ  and  D  are  constant  then    𝑥   ∝ 1/𝑑  ,  i.e.  the  fringes  get  closer  together  (for  a

given  colour,  say)  as  the  slit  separation  increases.  The  young  double-‐slit  experiment  i)

demonstrates  the  wave  nature  of  light  (since  only  waves  can  undergo  diffraction  and

interference),  ii)  enables  the  value  for  the  wavelength  to  be  determined  (by  measuring  ,  x,  d,

and  D  and  using  the  equation  𝜆 = (𝑥  ×𝑑)  /𝐷

Since  it  is  much  easier  to  obtain  a  pair  of  coherent  sources  of  sound  waves  then  an

analogues  experiment  can  be  performed  for  sound  waves.  The  primary  source  of  light  can

be  replaced  by  an  A.F.  (audio  frequency)  generator  and  the  double  slit  arrangement  can  be

replaced  by  a  pair  of  identical  speakers  connected  to  the  A.F.  generator.  In  place  of  the

screen,  a  detector  of  sound  waves  is  used  –  such  as  an  observer`s  ear  of  a  microphone

connected  to  a  cathode  ray  oscilloscope  (c.r.o)  or  to  a  speaker.

Coherent  water  waves  can  be  produced  in  a  ripple  tank  (using  dippers  or  barriers  with  gaps

in  them)  and  an  interference  pattern  obtained  and  observed.  In  fact,  ripple  tank

experiments  can  demonstrate  all  the  properties  of  reflection,  refraction,  diffraction  and

interference.  Also  all  waves  undergo  superposition.  In  fact,  only  waves  are  capable  of

undergoing  superposition.  In  fact,  only  waves  are  capable  of  undergoing  superposition

effects  such  as  diffraction  and  interference  –  particles  cannot  show  these  properties.