14 Waves 5

# 14 Waves 5 - Doppler effect moving source large low f...

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Doppler effect, moving source. Stationary Sound Source Source moving with v source < v sound ( Mach 0.7 ) Car horn small λ high f large λ low f

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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 λ = T v , where v is the wave speed. So the distance between the consecutive circles is λ . Imagine now moving your hand a distance Δ x during the time T . Then the distance between the consecutive circles in front of your hand will be λ = λ Δ x . And behind your hand the distance will be λ = λ + Δ x . Your hand is the source of waves here and its speed is u = Δ x / T . Therefore the distance between the circles is ) 1 ( ) / / 1 ( ) 1 ( ' v u T T x x x ± = Δ ± = Δ ± = Δ ± = λ λ λ λ λ λ λ
) 1 ( ' v u ± = λ λ The wave speed does NOT change, since the circles (wave crests), 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 What about the wave speed? does it change? What about frequency registered by an observer at rest? λ v f = v u f v u v v f / 1 / 1 1 ' ' ± = ± = = λ λ Here again “-” is for approaching source – higher frequency. “+” is for receding source – lower frequency.

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Police radar – sends frequency f . The car moving toward the radar at a speed u receives a frequency ) / 1 ( ' v u f f v u v f + = + = It reflects the received frequency f’ , but the car is a source moving toward the radar, so that the radar receives a frequency v u v u f v u f f / 1 / 1 / 1 ' ' ' + = = If u/v is small, which is typical for electromagnetic waves.

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