CONTENTS Important terms regarding wave motion Wave Sound waves Velocity of sound Wave motion Velocity of sound in elastic medium Reflection and refraction of waves Reflection of mechanical waves Progressive wave Principle of superposition Standing waves or stationary waves Standing waves on a string Standing wave in a closed organ pipe Standing waves in open organ pipes Vibration of a string Determination of unknown frequency Beats Doppler effect 16 1 16 2 16 3 16 4 16 5 16 6 16 7 16 8 16 9 16 11 16 12 16 13 16 14 16 15 16 16 16 17 16 18 16 19 16 10 Interference of sound waves Comparative study of stretched string and organ pipe 16 20 Some typical features of Doppler s effect in sound Sample Problems Practice Problems Basic and Advance Level Answer Sheet of Practice Problems Chapter 16 is known in An internationally acclaimed flautist of India Pandit Hariprasad Chaurasia is a very popular and eminent artiste for his outstanding who Indian popularising contribution Classical Music abroad His consummate artistry has distinguished him as the greatest living master of the North Indian bamboo Flute acclaimed both at home and abroad We can consider Flute as an organ pipe which are of two types closed and open Overall musical sound produced by an open organ pipe is sweeter than the musical sound produced by a closed organ pipe because in an open organ pipe all harmonics are present where as in a closed alternate pipe harmonics of frequency are present organ only 206 Wave Motion 16 1 Wave disturbed A wave is a disturbance which propagates energy and momentum from one place to the other without the transport of matter 1 Necessary properties of the medium for wave propagation i Elasticity So that particles can return to their mean position after having been ii Inertia So that particles can store energy and overshoot their mean position iii Minimum friction amongst the particles of the medium iv Uniform density of the medium 2 Characteristics of wave motion i It is a sort of disturbance which travels through a medium ii Material medium is essential for the propagation of mechanical waves iii When a wave motion passes through a medium particles of the medium only vibrate simple harmonically about their mean position They do leave their position and move with the disturbance iv There is a continuous phase difference amongst successive particles of the medium i e particle 2 starts vibrating slightly later than particle 1 and so on v The velocity of the particle during their vibration is different at different position vi The velocity of wave motion through a particular medium is constant It depends only on the nature of medium not on the frequency wavelength or intensity vii Energy is propagated along with the wave motion without any net transport of the medium mechanical waves waves 3 Mechanical waves The waves which require medium for their propagation are called Example Waves on string and spring waves on water surface sound waves seismic Wave Motion 207 4 Non mechanical waves The waves which do not require medium for their propagation are called non mechanical or electromagnetic waves Examples Light heat Infrared radio waves rays X rays etc 5 Transverse waves Particles of the medium execute simple harmonic motion about their mean position in a direction perpendicular to the direction of propagation of wave motion i It travels in the form of crests and troughs ii A crest is a portion of the medium which is raised temporarily above the normal position of rest of the particles of the medium when a transverse wave passes through it A E C Cre st i t a r b i V Particl e Normal n Level o B D Troug h Wave iii A trough is a portion of the medium which is depressed temporarily below the normal position of rest of the particles of the medium when transverse wave passes through it iv Examples of transverse wave motion Movement of string of a sitar or violin movement of the membrane of a Tabla or Dholak movement of kink on a rope waves set up on the surface of water v Transverse waves can be transmitted through solids they can be setup on the surface of liquids But they can not be transmitted into liquids and gases C C C T T Transverse wave in a rod Trough Crest Transverse wave on water surface Transverse wave in a string 6 Longitudinal waves If the particles of a medium vibrate in the direction of wave motion the wave is called longitudinal i It travels in the form of compression and rarefaction C R C R C R ii A compression C is a region of the medium in which Vibration of particle particles are compressed particles are rarefied iii A rarefaction R is a region of the medium in which 208 Wave Motion iv Examples sound waves travel through air in the form of longitudinal waves Vibration of air column in organ pipes are longitudinal Vibration of air column above the surface of water in the tube of resonance apparatus are longitudinal v These waves can be transmitted through solids liquids and gases because for these waves propagation volume elasticity is necessary 7 One dimensional wave Energy is transferred in a single direction only 8 Two dimensional wave Energy is transferred in a plane in two mutually Example Wave propagating in a stretched string perpendicular directions Example Wave propagating on the surface of water Example Light and sound waves propagating in space 16 2 Important Terms Regarding Wave Motion 1 Wavelength i It is the length of one wave 9 Three dimensional wave Energy in transferred in space in all direction ii Wavelength is equal to the distance travelled by the wave during the time in which any one particle of the medium completes one vibration about its mean position iii Wavelength is the distance between any two nearest particles of the medium vibrating in the same phase iv Distance travelled by the wave in one time period is known as wavelength v In transverse wave motion Distance between the centres of two consecutive crests Distance between the centres of two consecutive troughs Distance in which one trough and one crest are contained vi In longitudinal wave motion C Distance between the centres of two consecutive compression R C R C R C Distance between the centres of two consecutive rarefaction Distance in which one compression and one rarefaction contained 2 Frequency i Frequency of vibration of a particle is defined as the number of vibrations completed by particle in one second ii It is the number of complete wavelengths traversed by the wave in one second iii Units