DOPPLER EFFECT

This is the apparent change in the frequency of a wave motion as noted by an observer when there is relative motion between the source and the

observer .

The Effect is caused by the Motion of the source,

the observer, or both source and the observer.

1. MOVING SOURCEThis causes the wave crests to bunch up in front of

the source & the wave crests to be more widely spaced behind the source.

The overall effect is to cause a change in wavelength. The wave speed is not affected by the motion of the source.

2. OBSERVER MOVING

THIS CAUSES A CHANGE IN THE APPARENT WAVE SPEED.

There is no change in wavelength.

If the observer is moving towards the source, the speed of the wavefronts relative to him will be increased and he will receive more waves per second.

Moving away from the source the speed of the waves relative to him will be decreased and less waves will pass him per second .

OBSERVER

SOURCE STATIONARY

SOURCE

λ : CONSTANT,f : CONSTANT

OBSERVER

SOURCE MOVING TOWARDS OBSERVER

SOURCE

λ - REDUCED,f - INCREASED

OBSERVER

SOURCE MOVING AWAY FROM OBSERVER

SOURCE

λ - INCREASED,f - DECREASED

OBSERVER MOVING TOWARDS SOURCEMEETS MORE WAVES PER SECOND

SOURCE

The Effective Velocity of the waves is increased

OBSERVER MOVING AWAY FROM SOURCERECEIVES LESS WAVES PER SECOND

SOURCE

The Effective Velocity of the waves is reduced

SOURCE AND OBSERVER MOVING

SOURCE

BOTH WAVELENGTH AND EFFECTIVE WAVE VELOCITY ARE CHANGED

What does our friend hear?

VELOCITY OF SOURCE = WAVE VELOCITY

VELOCITY OF SOURCE > WAVE VELOCITY

E.g. crack when jet passes over.

Calculations using the Doppler Effect:

• Relative to the source:vw – vs = f’

(Where vw = speed of waves & vs = speed of source; ’ = shortened wavelength; f = wave frequency)

• Relative to the observer:vw = f’’

in this case the waves travel at a regular speed but with a higher frequency f’.

Dividing the first equation by the second we get:

f’ / f = [vw/ (vw- vs)]

To find the higher frequency i.e. in front of the

source:f’ = f [vw/ (vw- vs)]

To find the frequency behind the source:f’ = f [vw/ (vw+ vs)]

Combining these equations we get:f’ = f [vw/ (vw ± vs)]

Example 7:An ambulance travelling at a speed of 30.0ms-1 sounds a siren of frequency 400Hz. The speed of sound is 330ms-1. What frequency will an observer hear:a. As the ambulance approaches?b. As the ambulance moves away?

SOLUTION:a. As the ambulance approaches,

the apparent frequency is:f’ = f [vw/(vw – vs)]

= 400[330/(330 – 30.0)] = 132000/300

= 440Hz

b. As the ambulance moves away, the apparent frequency is: f’ = f [vw/(vw + vs)] = 400[330/(330 + 30.0)] = 132000/360 = 367Hz

APPLICATIONS

1. Red and blue shift

2. Speed cameras

3. Foetal blood pressure

4. Sonic boom

Red shift……………..The colour of light is related to its frequency / wavelength

1. RED/BLUE SHIFT IN LIGHT

RELATIVE MOTION BETWEEN SOURCE AND OBSERVER CHANGES THE COLOUR OBSERVED.

The emission and absorption lines of the light from distant stars and galaxies show a shift towards the red end of the spectrum as compared with those of the same elements in a laboratory source.

Astronomers use the Doppler effect, with respect to the colour spectrum, to determine the spin of stars and galaxies. If light is being emitted towards Earth then the frequency is high and it moves to the blue end of the spectrum hence blue shift. If light is receding then it tends to the lower frequency or red shift the degree of difference can determine the speed of spin. Spectral lines (lines of specific frequency) produced by elements in the stars can be viewed using a diffraction grating when this is compared with lines produced when light is shone through that element in a laboratory the degree of movement of that star/galaxy can be determined in relation to Earth.

This effect is called red shift . It is interpreted as due to recessional motion of the stars / galaxies from our solar system .

This suggests that the Universe is ??

EXPANDINGNote that it is possible for some close by stars

and galaxies to show a Blue Shift

Example 8:A line in the hydrogen spectrum has a frequency of 4.50 x 1014Hz when measured in laboratory experiments. The same line in light from a distant galaxy has a frequency of 4.40 x 1014Hz. Since the frequency fro the galaxy is lower, the galaxy must be moving away from the Earth. Calculate the velocity of the galaxy, vs.(Note that the speed of light is 3.00 x 108ms-1)

SOLUTION:f’ = f[vw/(vw+ vs)] [vw = the speed of light]vw + vs = (f x vw)/f3.00 x 108 + vs = (4.50 x 1014 x 3.00 x 108)/4.40 x 1014

3.00 x 108 + vs = 3.07 x 108

vs = 3.07 x 108 – 3.00 x 108

vs = 7 x 106ms-1

Source moving away

Red shifted light >>>>

Source moving towards

Blue shifted light >>>>

2. Radar speed detectors:• note the shift in frequency of microwaves

emitted from a speeding car.

3. Foetal blood pressure:where ultra sound is fired at the umbilical artery and the emitted sound then forms a trace that peaks and gradual declines. Size of range from peak to normal baseline determines blood pressure.

3. Sonic Boom:Sonic booms are produced when objects are moving faster than the speed of sound. In aircraft sound is produced by a rapid increase/decrease of air pressure. A cone is swept behind the plane with an increase in pressure at the nose (bow) and a decrease in pressure at the tail. As the plane passes a time delay causes the plane to pass a person standing still then the pressure hits them and a boom is heard. The larger the change in pressure the louder the boom. Small pressure changes e.g. supersonic bullets, bullwhips produce a ‘crack’.