- Progressive waves transfer energy from one place to another through a medium. Transverse waves have vibrations perpendicular to the propagation direction, while longitudinal waves have vibrations parallel. - For stationary waves formed by interference of progressive waves, nodes are points of no displacement and antinodes are points of maximum displacement. The distance between nodes and antinodes depends on the harmonic. - Organ pipes produce musical tones through stationary waves in a air column. Closed pipes have odd harmonics while open pipes have even harmonics. The fundamental and harmonic frequencies depend on pipe length and speed of sound.

1. Waves
Progressive waves

2. Progressive waves
● Waves that move energy from one place to other is called progressive wave.
● Transverse waves:
● The vibration of particles perpendicular to the propagation of energy of the wave .
● Longitudinal wave:
● The vibration of particles parallel to the propagation of the wave.

3. Displacement –distance
graph of both waves

4. Displacement –distance graph
● For transverse wave the graph is a snapshot of what is actually observed.
● For longitudinal wave the displacement is along the direction of distance but if these
displacements are plotted on y-axis, we will study the properties of wave without
considering the type of wave.

5. Displacement-time graph of a
point on a wave

6. phase and phase difference
● A term used to describe the relative positions of particles of a wave.
● For two points at distance d apart along a wave of wavelength λ
● The phase difference is equal to 2πd/ λ
●

7. Phase difference

8. PHASE

9. PHASE DIFERENCE
● If two oscillations are completely out of phase then the phase difference between them is
180 degree.
● when the crest or troughs of two different waves are aligned with each other then they are
said to be in phase.
● When a crest and trough of two waves are aligned then they are in anti-phase and have
phase difference of 180 degrees or π radian.
● 360 d/λ degrees or 2πd/ λ

10. Phase difference-d-t graph
● If two waves are out of step by a time t then the phase difference between them
● 2πt/T or 360t/T degrees.

11. Phase difference-d-t graph

12. Intensity of a wave
● The intensity of a wave is defined as the rate of energy transmitted (i.e. power) per unit area
at right angles to the wave velocity.
● intensity = power/cross-sectional area
● Intensity is measured in watts per square metre (W m−2)
● Intensity of a wave is directly proportional to square of its amplitude and square of its
frequency.
● Intensity of a wave is inversely proportional to square of its distance from the source.

13. Polarization

14. Polaroid

15. Doppler effect
● The whistle of a fast moving train appears to increase in pitch as it approaches a stationary
observer and it appears to decrease as the train moves away from the observer. this
apparent change in frequency was first observed and explained by Doppler in 1845
● The phenomenon of the apparent change in frequency of sound due to relative motion
between the source and the observer is called doppler effect.
● f0 = fs [v+/-V0]/[v+/-Vs]

16. Equations for observed
frequency
1.Source is moving towards the observer who is at rest
2.Source is moving away from the observer
3.Source is at rest and the observer is moving towards the
source
4.Source is at rest and the observer is moving away from the
source.
5.Source and the observer are moving towards the same
direction
6.Source and observer are moving towards each other
7.Source and the observer are moving away from each other.

17. Applications of Doppler effect
● An electromagnetic wave is emitted by a source attached to
a police car. The wave is reflected by a moving vehicle,
which acts as a moving source. There is a shift in the
frequency of the reflected wave. From the frequency shift
using beats, the speeding vehicles are trapped by the police
● RADAR (RADIO DETECTION AND RANGING)
● A RADAR sends high frequency radio waves towards an
aeroplane.The reflected waves are detected by the receiver
of the radar station.The difference in frequency is used to
determine the speed of an aeroplane.

18. Problem solving
● A railway engine and a car are moving parallel but in opposite direction with velocities 144
km/hr and 72 km/hr respectively.The frequency of engine’s whistle is 500 Hz and the
velocity of sound is 340 m s-1. Calculate the frequency of sound heard in the car when (i) the
car and engine are approaching each other (ii) both are moving away from each other.

19. Problem solving
● A police car travels towards the stationary observer at a speed of 15m/s.The siren on the
car emits a sound of frequency of 250hz.calculate the observed frequency .the speed of
sound is 340m/s.
● The sound emitted by a siren of an ambulance has a frequency of 1500Hz.the speed of
sound is 340m/s. calculate the difference in frequency heard by a stationary observer as the
ambulance travels towards and then away from the observer at a speed of 30m/s.

20. Electromagnetic waves
● An electromagnetic wave is a disturbance in the electric and magnetic fields in space
● infrared and ultraviolet waves – these lie beyond either end of the visible spectrum
● X-rays – these were discovered by Wilhelm Rontgen and were produced when a beam of
electrons collided with a metal target such as tungsten
● γ-rays – these were discovered by Henri Becquerel when he was investigating radioactive
substances.

21. Em wave

22. Electromagnetic waves

23. Red shift and blue shift
● Which allows astronomers to determine the speed at which
stars and galaxies are moving away from us, and which first
provided evidence that the Universe is expanding.
● if an astronomer looks at the light from a distant star which
is receding from Earth at speed vs, its wavelength will be
increased and its frequency will be decreased
● the light from the star will look redder than if it were
stationary. This is ‘red shift’.
● Decreased wavelength increased frequency , This is blue
shift.

24. Characteristics of wave motion
● (i) Wave motion is a form of disturbance travelling in the medium due to the periodic motion
of the particles about their mean position.
● (ii) It is necessary that the medium should possess elasticity and inertia.
● (iii) All the particles of the medium do not receive the disturbance at the same instant (i.e)
each particle begins to vibrate a little later than its predecessor.

25. continuation
● (iv) The wave velocity is different from the particle velocity. The velocity of a wave is
constant for a given medium, whereas the velocity of the particles goes on changing and it
becomes maximum in their mean position and zero in their extreme positions.
● (v) During the propagation of wave motion, there is transfer of energy from one particle to
another without any actual transfer of the particles of the medium.
● (vi) The waves undergo reflection, refraction, diffraction and interference.

26. Principle of superposition
● The principle of superposition states that when two or more waves meet at a point ,the
resultant displacement at that point is equal to the sum of the displacements of the
individual waves at that point.
● the resultant displacement is the algebraic sum of the displacements of waves A and B; that
is, their sum, taking account of their signs (positive or negative).
● It can be applied to more than two waves and also to all types of waves.

27. Adding two waves

28. Diffraction
● Diffraction is the spreading of a wave as it passes through a gap or around an edge.
● Diffraction effects are greatest when waves pass through a gap with a width roughly equal
to their wavelength

29. Diffraction of a wave

30. Interference

31. Interference

32. Constructive interference

33. Destructive interference

34. Interferences of waves
from two point sources

35. Equations of constructive
and destructive interference

36. Conditions for producing
observable interference pattern
● 1.the wave sources must have the same frequency
● 2.they must also have constant phase relationship
● The wave sources which maintain constant phase relationship are described as coherent
sources.
● the waves must have the same wavelength.
● It is not essential that both waves have the same amplitude to produce interference pattern
but in case of light a completely dark fringe would not be produced and the contrast of
pattern is reduced.

37. Coherent sources

38. Incoherent sources

39. Terms related to interference
● Maxima –maximum disturbance of waves
● Minima –minimum disturbance of waves
● Fringe –the maxima and minima disturbances are called fringes.
● The collection of fringes produced by the superposition of overlapping waves is called
interference pattern.

40. Young double slit
experiment
● https://www.youtube.com/watch?
v=nuaHY5lj2AA

41. Young double slit experiment

42. Fringe pattern in this
experiment

43. Interference pattern on
the screen

44. Conditions for bright
and dark fringe
● The condition for bright fringe to occur , the path difference should be nλ where n is the
whole number
● For the dark fringe to occur , the path difference is (n+1/2)λ
● The distance between successive bright fringes is called fringe width.
● The fringe width x =λD/a
● Where D is the distance between the screen and double slit
● a is the distance between the centre of the slits.

45. Problem solving
● Calculate the observed fringe width for a young’s double slit experiment using light of
wavelength 600nm and slits 0.5mm apart.the distance from the slits to the screen is 0.8m
● Calculate the wavelength of light which produces fringes of width 0.5mm on a screen 60cm
from two slits 0.75mm
● Radar waves of wavelength 50mm are emitted from two aerials and create a fringe pattern
1km from the aerials. Calculate the distance between the aerials if the fringe spacing is
80cm.

46. Single slit diffraction

47. Equation for single slit

48. Equation of first order
dark fringe

49. Equation of single slit
diffraction of light

50. Diffraction grating
● An arrangement consisting of a large number of equidistant parallel narrow slits of equal
width separated by equal opaque portions is known as a diffraction grating.
● It consists of a large number of equally spaced lines ruled on a glass or plastic slide. Each line
is capable of diffracting the incident light. There may be as many as 10 000 lines per
centimetre. When light is shone through this grating, a pattern of interference fringes is
seen.
● https://www.youtube.com/watch?v=764Fr0mnOrQ

51. Diffraction grating

52. Condition for maximum
intensity at an angle theta

53. Equation of maxima

54. Diffraction with white light

55. Stationary waves
● A stationary wave is the result of interference between two waves of equal frequency and
amplitude, travelling along the same line with the same speed but in opposite directions.
●

56. Stationary wave
● https://www.youtube.com/watch?v=-gr7KmTOrx0
● https://phet.colorado.edu/en/simulations/category/physics/sound-and-waves

57. Four modes of
vibrations of a string

58. Fundamental mode of a string

59. First harmonic
● The points where no vibration is called nodes.
● The point of maximum amplitude is called antinode.
● Nodes and antinodes do not move along the string.
● The note produced by the string vibrating in fundamental mode is given by f1=c/2L

60. Second harmonic or
first overtone

61. First overtone
● The frequency of this mode f2=c/L
● The wavelength of this mode is L
● The stationary wave pattern has 2 loops

62. Second overtone

63. Third harmonic
● The wavelength is 2L/3.
● The frequency is 3c/2L.
● The general expression for the nth mode or nth harmonic or (n-1) th overtone fn=nc/2L
where n=1,2,3…

64. Differences between progressive
and stationary wave
Progressive wave Stationary wave
Amplitude is same Amplitude is different
The crest and trough move along the
sting
The nodes and antinodes do not move
along
Particles of string attains maximum
displacement at different times
At the same time
There are only certain frequencies of
stationary waves.

65. Stationary waves
● The distance between any two
● successive antinodes or nodes is equal to
● λ/2
● and the distance between an antinode
● and a node is λ/4
● .

66. Vibrations of air
column in pipes
● Musical wind instruments like flute, clarinet etc. are based on the principle of vibrations of
air columns. Due to the superposition of the incident wave and the reflected wave,
longitudinal stationary waves are formed in the pipe.

67. Organ pipes
● Organ pipes are musical instruments which are used to produce musical sound by blowing
air into the pipe. Organ pipes are two types (i) closed organ pipes, closed at one end (ii) open
organ pipe, open at both ends.

68. Closed organ pipe
● If the air is blown lightly at the open end of the closed organ pipe, then the air column
vibrates (Fig. 7.16a) in the fundamental mode. There is a node at the closed end and an
antinode at the open end. If l is the length of the tube,
● If f1 is the fundamental frequency of the vibrations and c is velocity then f1=c/4l

69. Closed organ pipe

70. Overtones
● If air is blown strongly at the open end, frequencies higher than fundamental frequency can
be produced. They are called overtones.
● f3=c/λ3 ,=3c/4L first overtone , or third harmonic
● f5=c/λ5 ,=5c/4L second overtone or fifth harmonic
● Therefore the frequency of pth overtone is (2p + 1) f1 where f1 is the fundamental frequency.
In a closed pipe only odd harmonics are produced. The frequencies of harmonics are in the
ratio of 1 : 3 : 5.....

71. Overtones

72. Open organ pipe
● When air is blown into the open organ pipe, the air column vibrates in the fundamental
mode
● Antinodes are formed at the ends and a node is formed in the middle of the pipe. If l is the
length of the pipe, then l= λ/2
● The fundamental frequency f1=v/2L

73. Open organ pipe
/fundamental mode

74. First overtone /second
harmonic

75. Second overtone

76. First overtone /equation
● The fundamental frequency for first overtone is
● f2=2f1
● The fundamental frequency for second overtone is
● f3= v/λ3, λ3=2l/3 =3f1.
● Therefore the frequency of Pth overtone is (P + 1) f1 where f1 is the fundamental frequency.
● The frequencies of harmonics are in the ratio of 1 : 2 : 3 ....