1. Doppler Effect The apparent change in the frequency of sound, caused by the relative motion between the source of sound and the observer, is called Doppler effect.

2. The Doppler effect (or Doppler shift), named after Austrian Scientist Christian Doppler who proposed itAustrianChristian Doppler in 1842. Born 29 November 1803(1803-11-29) Salzburg, Austria SalzburgAustria Died 17 March 1853 (aged 49) Venice, Italy VeniceItaly Doppler Effect

3. nana = V V × n Doppler Effect  VsVs  VsVs

4. Source is moving towards observer Case I : 1. Observer is stationary (V 0 = 0) and source is in motion Source is moving away from observer2. nana = V V × n –VsVs nana = V V +VsVs nana = V V  VsVs  VsVs

5. Observer is moving towards source. Case II : 1. Source is stationary (V s = 0) and observer is in motion. Observer is moving away from source2. nana = V V × n +V0V0 nana = V V –V0V0 nana = V V  VsVs  VsVs

6. Moving towards each other Case III : 1. Both source and observer is in motion Moving away from each other2. nana = V V × n +V0V0 –VsVs nana = V V –V0V0 +VsVs nana = V V  VsVs  VsVs

7. T/2 T/4 + a 0 – a 3T/4 5T/4 T T/2 T/4 + a 0 – a 3T/4 5T/4 T + T/2 + 2a 0 – 2a 3T/4 5T/4 T T/4

8. Note : Resultant amplitude is given be R = a 2 1 + a 2 2 + 2a 1 a 2 cos (a 1 – a 2 )  Resultant amplitude is given be R = (a 1 – a 2 )  a1a1 = a2a2 If = a R = 2a  I max  (a 1 + a 2 ) 2 OR I max  4a 2 (if a 1 = a 2 = a)

9. T/2 T/4 + a 0 – a 3T/4 5T/4 T T/2 T/4 + a 0 – a 3T/4 5T/4 T +

10. Note : Resultant amplitude is given be R = a 2 1 + a 2 2 + 2a 1 a 2 cos (a 1 – a 2 )  The phase difference is 180 0, (a 1 – a 2 ) = 180 R = (a 1 – a 2 )  a1a1 = a2a2 If = a R = 0  I max  (a 1 + a 2 ) 2 OR I max =0 (If a 1 = a 2 = a)

11. Formation of Beats. Superposition of Waves Intercity is minimum Intercity is minimum Waves are in same direction There is a slight difference in frequency

14.  It is also defined as the number of waves emitted per second by the source. Frequency (n) :  It is number of oscillations performed in one second by a particle of a medium OR  S.I unit : Hertz ( Hz) = n 1 __ T

15.  Distance travelled by the wave per unit time.  S.I Unit : meter/second Speed (v) = Distance time = λ T = T 1 × λ = n λ v Wave velocity (v) :  In one period (T), wave covers a distance equal to one wavelength

18. y a sin = – 2x 2x 2  nt  = 2n 2n (2) y a sin2  = – x nt nt But, y a sin2  = – x t T Now,n = 1 T (3) v n = n =  v