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Case #1 – moving observer.

Doppler effect – change in the wave frequency and/or wave length due to motion of the source or the observer (or both). Case #1 – moving observer. L. The train is moving at a speed v , and the cars have a length L . When the observer is at rest there are. cars passing by every second.

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Case #1 – moving observer.

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  1. Doppler effect – change in the wave frequency and/or wave length due to motion of the source or the observer (or both). Case #1 – moving observer. L The train is moving at a speed v, and the cars have a length L.When the observer is at rest there are cars passing by every second

  2. Doppler effect – change in the wave frequency and/or wave length due to motion of the source or the observer. Case #1 – moving observer. L The train is moving at a speed v, and the cars have a length L.When the observer is moving in the same direction as the train at a speed u, the relative speed is v – u and there are cars passing by every second

  3. Doppler effect – change in the wave frequency and/or wave length due to motion of the source or the observer. Case #1 – moving observer. L The train is moving at a speed v, and the cars have a length L.When the observer is moving in the direction opposite to the train at a speed u, the relative speed is v + u and there are cars passing by every second

  4. l With “+” and “-” corresponding to the opposite and same directions of motion, respectively.The wave length does not change (of course!), but the relative velocity does. + ­ The general equation is The original frequency is Therefore,

  5. Doppler effect. large l small l high f low f Source moving with vsource<vsound ( Mach 0.7 ) Stationary Sound Source Car horn

  6. Case #2 – moving source. Imagine splashing water with time intervals T, and making a circular wave every T seconds. In the time intervals between two consecutive splashes, a circle travels a distance l= Tv, where v is the wave speed.So the distance between the consecutive circles is l. Imagine now moving your hand a distance Dx during the time T. Then the distance between the consecutive circles in front of your hand will be l’= l –Dx.And behind your hand the distance will be l’= l +Dx.Your hand is the source of waves here and its speed is u=Dx/T.Therefore the distance between the circles is

  7. Case #2 – moving source. The wavelength changes if the source of the waves moves.It decreases if the source and the wave move in the same direction (approaching source) The wavelength increases if the source moves in the direction opposite to the wave motion (receding source), “+” in the equation. Red light has a larger wavelength than green or white light. What about the wave speed? does it change?What about the frequency registered by an observer at rest?

  8. What about the wave speed? does it change?What about frequency registered by an observer at rest? The wave speed does NOT change, since the circles, once generated, loose any connection with the source, and cannot “know” about motion of the source. They only care about the mechanical properties of the medium.Therefore the wave length and the frequency are connected by the usual equation Here again “-” is for approaching source – higher frequency.“+” is for receding source – lower frequency.

  9. Doppler effect. large l small l high f low f Source moving with vsource < vsound ( Mach 0.7 ) Stationary Sound Source Car horn

  10. Police radar – sends frequency f. The car moving toward the radar at a speed u receives a frequency It reflects the received frequency f’, but it is a source moving toward the radar, so that the radar receives a frequency If u/v is small, which is typical for electromagnetic waves. The frequency of the received signal is higher by

  11. Why the equations for moving source and moving observer are different ? Isn’t any motion relative? There is third player in the game – the medium for the waves. It makes a lot of difference, whether or not the source of the wave moves with respect to the material medium. The mechanical waves (surface waves, string waves, sound etc.) absolutely need a material medium to propagate.Any waves that do not need a material medium?

  12. Electromagnetic waves can propagate in vacuum and do not require any medium. Does it make any difference?A lot of difference! The whole theory of relativity can be derived from it. For light and other electromagnetic waves only the relative velocity of the source and the observer matter.If this velocity is much lower than the speed of light, c (the normal situation), the equations become: The upper sign is for motion away from each other;the light becomes more red.The lower sign is for motion toward each other;the light becomes more violet.

  13. Waves from a source, which is receding from us, are perceived to have lower frequency and larger wavelength. Red shift (shift toward larger wavelengths) in the spectra of distant galaxies is an evidence of expanding universe.

  14. Shock waves – sonic booms. Source moving with Vsource=Vsound ( Mach 1 - breaking the sound barrier ) Source moving with Vsource>Vsound (Mach 1.4 - supersonic) The shock waves are radiated by ANY object moving through a medium at a speed about the speed of waves in the medium, e.g. speed of sound.In other words, even object not emitting any waves at rest becomes a source of shock waves at a supersonic speed.

  15. Shock waves. Mach cone.

  16. Shock waves. Mach cone. A triangle in the cone:a side a= Tv – the travel distance of the wave within one period. v a q b u The hypotenuseb =Tu– the travel distance of the moving object. q - the Mach angle - Mach number The sharper the Mach angle, the higher the speed of the object

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