Doppler Effect

The Doppler effect is the apparent change in the frequency of a wave motion when there is relative motion between the source of the waves and the observer.The apparent change in frequency f experienced as a result of the Doppler effect is known as the Doppler shift.The value of the Doppler shift increases as the relative velocity v between the source and the observer increases. The Doppler effect applies to all forms of waves.

http://www.colorado.edu/physics/2000/applets/doppler.html

Suppose the source moves at a steady velocity vs towards a stationary observer.

The source emits sound wave with frequency f. From the diagram, we can see that the distance

between crests is shortened such that sv'

vs

Since = c/f and = 1/f,We get

f

v

f

c

f

c s'

fvc

cf

s

)('

Doppler Effect (Moving Source)

http://sci.esa.int/content/doc/16/28950_.htm

Consider an observer moving with velocity vo toward a stationary source S.

The source emits a sound wave with frequency f and wavelength = c/f.

The velocity of the sound wave relative to the observer is c + vo.

fc

vcvcf oo

/'

fc

vf o )1('

c

Doppler Effect (Moving Observer)

Doppler Shift

Consider a source moving towards an observer, the Doppler shift f is

fff ' ffvc

c

s

)(

s

s

vc

v

f

f

If vs<<c, then we getc

v

f

f s

The above equation also applies to a receding source, with vs taking as negative.

Doppler Effect (Moving Reflector) [1]

When a sound wave is reflected from a moving object, the frequency of the reflected wave will be different, because of the Doppler effect, from that of the incident wave.

Consider a sound wave of frequency f is directed toward an object moving with a speed v toward the stationary source.

f f’

f’f”

Transmitter

Receiver

v

Reflectingsurface

Doppler Effect (Moving Reflector) [2]

For the outward journey, the source is stationary and the observer (reflecting surface) is moving.

fc

vcf )('

For the return journey the source (reflecting surface) is moving and the observer is stationary.

'" fvc

cf

Combining the two equations gives

fvc

vcf )("

The Doppler effect can be summarized qualitatively :

The observed frequency of sound is increased whenthe source and observer are approaching each other and is decreased when they are receding from each other.

Or mathematically,

fvc

vcf

s

o )('

Summary of the Doppler Effect

• Ultrasonic waves reflected from red blood cells can be used to determine the velocity of blood flow.

• Reflection of ultrasonic waves can also be used to detect the movement of the chest of a young fetus and to monitor its heartbeat.

Applications of Doppler Effect (Medicine)

• The velocities of distant galaxies can be determined from the Doppler shift ( The apparent change in frequency). • Light from such galaxies is shifted toward lower frequencies, indicating that the galaxies are moving away from us. This is called the red shift.

Applications of Doppler Effect (Astronomy)

Redshift

Blue shift

Applications of Doppler Effect (Radar Speed Trap)

The police monitor the speeds of vehicles with radar gun. The radar gun send microwaves towards the car. The wave reflected back to the gun have a higher frequency because of the Doppler effect.The microwave receiver in the radar gun detects the difference in frequency f between the emitted signal and the received signal. The speed of the car is calculated from this, and displayed automatically on a screen.

Sonic Boom (Shock Waves)

If a source of sound moves faster than the speed of sound a shock wave occurs.

http://hyperion.advanced.org/19537/java/Doppler.html