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When the source of a wave and an observer move either towards or away from each other the observed frequency of the wave will be different from the frequency at which the wave is emitted. For example, if you are standing by the side of the road and a police car with a siren passes by, the frequency of the sound you hear will be higher when the car is moving towards you and lower when it is moving away from you. This is called the Doppler Effect. Consider a stationary source that emits waves at some constant frequency fs. The waves move at a constant speed v through the medium. If that source starts to move at a constant speed vs (relative to the medium) towards an observer, it willcatch up with the wave crests that it emits, so that the wave crests will be closer together (the wavelength will be shorter) and the observed frequency, fo, will be higher. (a) Show that the frequency observed when a wave source moves either towards or away from a stationary observer with speed vs relative to the medium is given by: Determine when the sign will be positive or negative. (b) An observer moves towards/away from a source with speed vo relative to the medium Show that the observed frequency is given by: Determine when the sign will be positive or negative. Hint: Think relative velocities!

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The apperent change in frequency of sound due to relative motion between the source and observer is called doppler shift. (1) If observer at st o 0),and source at rest (v, 0)at rest,there is no apperent change in frequency of sound heared by the observer 10 Here.j, is frequency of the source (car), vis velocity of sound in air Ais the wavelength of the source If the source moving with a velocity(v,) in the time (Fo)relative to the observer, the shiftinwavelength is The shift in frequency is here ere J0 !-드 vtv If the source moves towords the obserever shift if the source moves away from the obserever shift fJ

If the observer is moving with a velocity (vo) and source is at rest,the time interval he will measures between meeting successive crests are Shift in frequency is here =- vtv If the observer moves towords the source shift |j v一场 if theobserver moves away from the source shift |f-

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