Doppler Effect

Imagine a Formula 1 car approaching the stands at 60m/s. The frequency of sound made by the engine as heard by a stationary observer in the stands is higher than the actual frequency as heard by the driver. The sound is squashed up – or better, the apparent wavelength is decreased and the apparent frequency increased.

car approaching observer
car receding from observer

 

As the car recedes away from the stands, exactly the reverse happens. the observer waves goodbye to the red line. Think of EEEEYOWWWW as the car approaches then recedes.

For a stationary observer and a moving source, we can write:

These will mostly do – but IB requires us to use these as well:-A quick calculation shows how the first equation works. Let the car be moving towards us in the stands at a speed us of 60m/s and emitting a frequency f of 800Hz.

Speed of sound in air is 340m/s. We can find the frequency f’ as heard by the stationary observer. Common sense tells us whether we add or subtract the velocities – in this case, we subtract and hear a higher frequency as it approaches us. (the EEEE bit)

 

As it recedes, we add, thus: (the YOWWW bit)

Police speed detectors bounce microwave radiation (about 10GHz) off a moving vehicle and detect the reflected waves. Because the car is moving towards the police observer, these waves are shifted in frequency by the Doppler effect and the difference in frequency between the transmitted and reflected waves provides a measure of the vehicle’s speed. Of course it works just as well for recession speeds as well.

Two Doppler shifts because of the reflection from a moving target. c is of course the speed of light

By observing distant galaxies, Edwin Hubble concluded that distance and recession speed were proportional – so galaxies further away are receding faster than closer galaxies. We know this because the atomic fingerprint or spectrum of atomic hydrogen or helium is shifted to the red (long wavelength) end of the visible spectrum. The degree of redshift can be used to find out how far away a galaxy is.

This absorption spectrum shot (idealised) shows what the spectrum of atomic hydrogen might look like from several distant objects like galaxies. The further away, the greater the redshift. Redshifts of up to 0.95c have been observed – the light having taken almost the lifetime of the Universe to reach us.

 

 

Finally, a medical use. Doppler blood flow is a technique whereby ultrasound waves (f about 800Hz) emitted from a piezoelectric transducer (transmitter/receiver) are reflected off red blood cells in an artery or vein as they are moving towards the stationary detector. The more occluded or blocked the artery is (think about a fluid in a pipe) the faster the cells are moving. It can also be used to find blood clots in deep veins – DVT – deep vein thrombosis – can be fatal.

The detector and the moving cells are at an angle hence the cosine term and, like the police car, the factor 2 accounts for the reflection from a moving source.

 

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