Doppler EffectDoppler Effect

DEFINITIONDEFINITION

First explained in 1842 by First explained in 1842 by Christian DopplerChristian Doppler, the , the Doppler EffectDoppler Effect is the shift is the shift in frequency and wavelength in frequency and wavelength of waves which results from of waves which results from a source moving with a source moving with respect to the medium, a respect to the medium, a receiver moving with receiver moving with respect to the medium, or respect to the medium, or even a moving medium.even a moving medium.

DEFINITIONDEFINITION

In other words, the In other words, the Doppler Doppler Effect refers to the Effect refers to the change in pitch of a sound change in pitch of a sound due to the motion either due to the motion either of the source or of the of the source or of the listener.listener.

Moving SourceMoving Source

Sound moves equally in all directions from a source.Sound moves equally in all directions from a source.• Circular (or spherical) patternCircular (or spherical) pattern

If the source is moving the origin of successive If the source is moving the origin of successive circles moves.circles moves.

CHARACTERISTICS OF THE CHARACTERISTICS OF THE DOPPLER EFFECTDOPPLER EFFECT

If two objects are approaching each other, or if If two objects are approaching each other, or if an initial object is approaching a second standing an initial object is approaching a second standing object, the pitch is higherobject, the pitch is higher

If two objects are moving apart, or if an initial If two objects are moving apart, or if an initial object is moving apart from a second standing object is moving apart from a second standing object, the pitch is lowerobject, the pitch is lower

SoundSound

The Doppler effect causes the changing pitch of a siren.

When a firetruck approaches, the pitch sounds higher than normal because the sound wave crests arrive more frequently.

When the firetruck passes and moves away, you hear a drop in pitch because the wave crests are arriving less frequently.

The Doppler Effect

Note: The change in loudness is not the Doppler Effect! It is the shift in frequency!

EQUATIONEQUATION The perceived frequency (The perceived frequency (ff ´) is related to the ´) is related to the

actual frequency (actual frequency (ff00) and the relative speeds of ) and the relative speeds of the source (the source (vvss), the speed (), the speed (vv) of waves in the ) of waves in the medium by an equation:medium by an equation:

ff22 = fo ( v/ v+ v = fo ( v/ v+ vss) ) if the source is moving away from the observerif the source is moving away from the observer

ff22 = fo ( v/ v- v = fo ( v/ v- vss) ) if the source is moving toward the observerif the source is moving toward the observer

EXPLANATIONEXPLANATION The choice of using the plus (+) or minus (-) The choice of using the plus (+) or minus (-)

sign is made according to the convention sign is made according to the convention that if the source and observer are moving that if the source and observer are moving towardstowards each other the perceived each other the perceived frequency (frequency (ff ´) is ´) is higherhigher than the actual than the actual frequency (frequency (ff00). Likewise, if the source and ). Likewise, if the source and observer are moving observer are moving away fromaway from each other each other the perceived frequency (the perceived frequency (ff ´) is ´) is lowerlower than than the actual frequency (the actual frequency (ff00). ).

Sample problemSample problem A car travelling at 100 km.hr sounds its horn as it A car travelling at 100 km.hr sounds its horn as it

approaches a hiker standing on the highway. If the approaches a hiker standing on the highway. If the car’s horn has a frequency off 44o Hz and the car’s horn has a frequency off 44o Hz and the temperature of the air is 0 C what is the frequency of temperature of the air is 0 C what is the frequency of the sound waves reaching the hiker?the sound waves reaching the hiker?

Activity # 7: Doppler ShiftActivity # 7: Doppler Shift You are standing at a railway. A train approaching at You are standing at a railway. A train approaching at

125 km/h sounds its whistle. If the frequency of the its 125 km/h sounds its whistle. If the frequency of the its whistle s 442 Hz and the air temperature s 20 C whistle s 442 Hz and the air temperature s 20 C what frequency do you hear when the train what frequency do you hear when the train approaches you? when the train has passed by you?approaches you? when the train has passed by you?

A car sounds its horn (502 Hz) as it approaches a A car sounds its horn (502 Hz) as it approaches a pedestrian by the side of the road. The pedestrian pedestrian by the side of the road. The pedestrian has perfect pitch and determines that the sound from has perfect pitch and determines that the sound from the horn has a frequency 520 Hz. If the speed of the horn has a frequency 520 Hz. If the speed of sound that day was 340 m/s how fast was the car sound that day was 340 m/s how fast was the car travelling?travelling?

Sonic BoomSonic Boom

The speed of sound is called The speed of sound is called Mach 1.Mach 1.

Faster than that speed Faster than that speed causes a shock wave – a causes a shock wave – a sonic boom.sonic boom.

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Shock WaveShock Wave

A moving source can A moving source can exceed the speed of exceed the speed of sound.sound.

The sound waves The sound waves constructively interfere on constructively interfere on a front at an angle to the a front at an angle to the motion.motion.

This is called a This is called a shock shock wavewave..

Police use the Doppler effect of radar waves to measure the speeds of cars on the highway.

Radar waves are electromagnetic waves.

Police bounce them off moving cars. A computer built into the radar system compares the frequency of the radar with the frequency of the reflected waves to find the speed of the car.

The Doppler Effect

LightLight

The Doppler effect also occurs for light.• When a light source approaches, there is an

increase in its measured frequency.• When it recedes, there is a decrease in its

frequency.

The Doppler Effect

Increasing frequency is called a blue shift, because the increase is toward the high-frequency, or blue, end of the spectrum.

Decreasing frequency is called a red shift, referring to the low-frequency, or red, end of the color spectrum.

Distant galaxies show a red shift in their light. A measurement of this shift enables

astronomers to calculate their

speeds of recession. The red shift

Is also a piece of evidence for the

Big Bang theory.

The Doppler Effect

When a source moves toward you, do you When a source moves toward you, do you measure an increase or decrease in wave speed?measure an increase or decrease in wave speed?

The Doppler Effect

How does the apparent frequency of waves change as a wave source moves?

The Doppler Effect