# Doppler Effect

As discovered by Christian Doppler

There is a video here, but this time we dont need to watch it,

in fact if we are to make the most of it close your eyes,

we'll play the video and discuss what we heard

This is an example of the Doppler Effect

ANOTHER EXAMPLE

Take an electronic buzzer and battery so when connected will make a buzzing noise.

Attach the apparatus to a length of elastic.

Carefully spin the buzzer et al in a horizontal circle,

Students will here the buzzer changing pitch as it approaches them and recedes from them.

Watch the following applet play through

What do you think now ?

http://www.walter-fendt.de/ph14e/dopplereff.htm

Qualitative treatment.

So if some machine makes a constant noise or regularly altering set of sounds (as a siren) then we can represent the sound to travel in equally spaced wavefronts. As long as the source of the sound remains stationary

but what happens when it moves ??

As you should have noticed in the applet that the waves come from the car as per usual, but as the car moves toward the observer these wavefronts seem closer to each other,

thus shortening the wavelength ......

...... thus raising the pitch of the sound

but as the ambulance passes the observer, again the waves seem to lengthen as the source of the wave is has been moved away from the last wave front

the change in the pitch is easily calculated, this is a multiple of the original frequency.

this multiple is the same as the ratio of the actual speed of the wave over the speed less the speed of the vehicle is coming towards us and added going away

Source Approaching Observer

Source and Observer going away

Simple quantitative treatment for moving source and stationary observer.

Appropriate calculations without deriving formula.

A Siren on an ambulance wails at 1000Hz when it is standing still, calculate the pitch of the siren if the ambulance is approaching you at 30m/s

and after when it maintains the speed and continues away what will be the frequency of the sound then

page 188 more examples, complete the questions on page 190

Applications of the Doppler effect

Speed traps.

Handheld and tripod mounted laser guns

A Laser pulse is sent out from the gun,

A CCD (digital camera) in the gun detects the frequency of the reflected light

by using the doppler formula the speed trap equipment gives back a speed that the car is travelling at

Handheld 'radar' gun: 35.1 GHz signal, 0-300 mph speed range, 0.1 mph sensitivity, 30 Hz sampling rate.

Blue shift / Red shift of stars.

due to the motion of stars relative to earth, the characteristic spectra of these stars gets shifted as to have a slightly different frequencies than we would expect

It was Edwin Hubble that is credited with the discovery that the universe is expanding. In 1903 Hubble and Vesto Slipher noticed there was a reddness

of the stars that the frequencies of light had all been reddened. By using the Doppler formulae it can be seen that this can only be explained if the stars

are going away from the observer.

http://en.wikipedia.org/wiki/File:Suzredshift.gif

of course red shift does not make the stars look red ....

Demonstration of the Doppler effect in a Lab.

A Question

(a) A motorist was caught driving past a traffic light while it was still red. At his trial he claimed that he was driving so quickly that the light appeared green to him due to the Doppler effect and so he should be acquitted. The judge, who had recently studied S104, accepted his argument but said that he had clearly been speeding so he would have to fine him for that. He continued (with a smile) that because he was feeling generous that he would only fine him 1 pence for each km hr−1 at which he had been travelling. (Note that 100 pence = UK £1.)

(i) Combine and rearrange Equations to produce an equation relating the speed of the motorist to the shift in wavelength of the light emitted by the traffic light.

(ii) By choosing appropriate wavelengths for red (610 x 10-9) and green light (520 x 10-9)to two significant figures calculate the size of the fine for the lucky(!) motorist.

(b) Astronomers studying the rate at which the Universe is expanding make use of observations of Type Ia supernovae. These are the results of the explosions of an object called a white dwarf (which is the dead core of a star of similar mass to the Sun). These are very important as it is thought that all Type Ia supernovae have the same intrinsic luminosity. Assuming this to be the case, what would be the ratio of the brightness of two Type Ia supernovae, one observed in galaxy A, with a redshift of 0.8, and one in galaxy B, with a redshift of 0.2, as seen from the Earth?

(c) The James Webb Space Telescope is NASA’s successor to the Hubble Space Telescope (HST) and is due to launch in 2013–14. One of the main goals of this telescope is to detect and study the first galaxies that formed in the Universe and consequently it is designed to be much more sensitive to infrared light than the HST. Considering your answers to parts (a) and (b) briefly describe the reason for this design feature. (We expect you will be able to answer in no more than 120 words.)