Title WAVE MOTION & DOPPLER'S EFFECT.pdf ✅

 Digital www.allendigital.in [ 183 ] Introduction and Classification of Waves What is wave motion? A wave is a disturbance which transports energy and momentum both from one point to another without the transport of matter. Few examples of waves: The ripples on a pond (water waves), the sound we hear, visible light, radio and T.V. signals etc. (i) Based on necessity of medium: A wave may or may not require medium for its propagation 1. The waves which do not require medium for their propagation are called non-mechanical or electromagnetic waves. Examples : Light, radio waves etc. 2. The wave which require medium for their propagation are called mechanical wave. Examples : Waves in string etc. Note: In propagation of mechanical waves elasticity and density of the medium play an important role therefore mechanical waves are also known as elastic waves. (ii) Based on energy propagation: Wave can be divided into two parts on the basis of energy propagation. 1. Progressive Wave: The waves in which energy propagate in a medium or space with constant speed. 2. Stationary wave: The waves in which the particles of medium vibrates with different amplitude but energy does not propagate. (iii) Based on dimensions Wave can be one, two or three dimensional according to the number of dimensions in which they propagate energy. 1. One dimensional wave (1-D): Waves moving along strings are one dimensional wave. 2. Two dimensional wave (2-D): Surface waves or ripple on water is two dimensional waves. 3. Three dimensional wave (3-D): Sound waves, light waves are three dimensional waves. (iv) Based on vibration of particle: Waves are of two types on the basis of motion of particle of the medium. Wave Classification According to Necessity of medium Propagation of energy Dimensions Vibration of particle (i) Elastic or mechanical waves (ii) E.M. waves or non-mech. (i) Progressive (ii) Stationary (i) One dimensional (ii) Two dimensional (iii) Three dimensional (i) Transverse (ii) Longitudinal Wave Motion and Doppler's 03 Effect
NEET : Physics [ 184 ] www.allendigital.in  Digital (1) Transverse wave : In transverse wave the direction of vibration of particle is perpendicular to the direction of propagation of wave. • Mechanical transverse waves are produced in such type of medium which have shearing property, so they are known as shear wave or S-wave. • Shearing is the property of a body by which it changes its shape on application of force. • Mechanical transverse waves are generated only in solids and surface of liquid. This wave propagates in form of crest and trough. (2) Longitudinal Wave : In this wave the direction of vibration of particle is along the direction of propagation of wave. • Oscillatory motion of the medium particles produces region of compression (high pressure) and rarefaction (low pressure) which propagated in medium with time. • The region of high particle densities are called compressions and region of low particle densities are called rarefactions. Illustration 1: Given below are some example of wave motion. State in each case whether the wave motion is transverse, Longitudinal or a combination of both? (1) Motion of kink in a long coil spring produced by displacing one end of the spring sideways. (2) Wave produced in a cylinder containing a liquid by moving its piston back and forth. (3) Wave produced by a motorboat sailing in water. (4) Ultrasonic waves in air produced by a vibrating quartz crystal. Solution: (1) Transverse and longitudinal (2) Longitudinal (3) Transverse and longitudinal (4) Longitudinal Direction of disturbance vibration Direction of propagation Trough Direction of travel Equilibrium position Crest Direction of disturbance Direction of propagation compressions rarefactions
Wave Motion and Doppler's Effect  Digital www.allendigital.in [ 185 ] Illustration 2: Mechanical waves in gaseous medium are: (1) Transverse (2) Neither transverse nor longitudinal (3) Longitudinal (4) Either transverse or longitudinal Solution: A wave moving in a gas must be longitudinal and not transverse because longitudinal sound wave can travel through a gas. Hence (3) is correct. Illustration 3: Water waves are of the nature: (1) Transverse (2) Longitudinal (3) Sometime longitudinal and sometimes transverse and longitudinal both. (4) Neither transverse nor longitudinal Solution: Water molecules displace along the propagation direction as well as along perpendicular direction. Hence both longitudinal and transverse. Hence (3) is correct. Illustration 4: Which of the following statement is correct? (1) Both light and sound waves in air are transverse. (2) The sound waves in air are longitudinal while the light waves are transverse. (3) Both light and sound waves in air are longitudinal (4) Both light and sound waves can travel in vacuum. Solution: Light waves are E.M. wave. Sound wave is longitudinal wave. Hence (2) is correct. Some important terms connected with wave motion. (1) Wave length (λ) : It is the distance between two successive crest or two successive troughs. It can also be defined as the distance travelled by the wave during the time interval in which any one particle of medium completes one cycle about its mean position. (2) Frequency (f, n) : Number of cycle (number of complete wavelengths) completed by a particle in unit time. (3) Time Period (T) : Time taken by wave to travel a distance equal to the wavelength. (4) Amplitude (A) : Maximum displacement of vibrating particle from its equilibrium position. Trough Wave length Equilibrium position Crest Amplitude A
NEET : Physics [ 186 ] www.allendigital.in  Digital (5) Angular frequency (ω) : It is defined as, 2 2 n T   = =  . (6) Phase: Phase is a quantity which contains all information related to any vibrating particle in a wave. For equation y = Asin(ωt – kx) ; ωt – kx → Phase. (7) Angular wave number (k) : Angular wave number or propagation constant is denoted by 2 k  =  . The S.I. unit of ‘k’ is radian/meter. (8) Wave number (ν̅): It is defined as number of waves in unit length of the wave pattern. 1 k v 2 = =   (9) Wave velocity (v): The velocity with which the disturbance travel through the medium is called wave velocity. V T  = Above formula can be written as: 2 v 2 T     =  =       v 2  =    2 v k k     = =      Graph between angular frequency () and wave number (ν̅): ( ) 1 v wave length =  As we know that, ω = 2n ; v = n v  = 2   1     v Illustration 5: A progressive wave of frequency 500 Hz is travelling with velocity 360 m/s. Find the wavelength of wave? Solution: We know that for a wave, v = f λ so, v 360 0.72m f 500  = = = Illustration 6: On the average human heart is found to beat 75 times in a minute. Calculate its frequency of heart and its period? Solution: The beat frequency of heart 75 1.25 Hz 60 = = and Time period 1 1 T 0.8 sec f 1.25 = = = Illustration 7: A thunder tap is heard 7.5 sec after the lighting flash. The distance of the flash is (Speed of sound is 330 m/sec) Solution: Distance d = Speed × time  d = (330) (7.5) = 33 × 75 = 2475 m  v̅