Download Measuring the Doppler effect in the classroom

Measuring the Doppler Effect in the classroom
The most accurate method for detecting exoplanets is the radial velocity method. This relies on measuring
the Doppler shift in light from a star as its position is changed due to the gravitational field of the orbiting
planet(s). With stars, we look at their spectra to detect small shifts in the frequency of the light detected.
𝑐
𝑓𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 = (
)𝑓
𝑐 + 𝑣𝑠𝑡𝑎𝑟 𝑠𝑜𝑢𝑟𝑐𝑒
Measuring the Doppler using light in the classroom is not possible, due to the high speed of light
(300,000,000 ms-1). However, using sound at 340 ms-1, this becomes practicable.
Free signal generator apps can now be found for iOS and Android to produce a stable tone. Free software
can also been downloaded that will allow analyses of frequency spectra.
In this example, I used FuncGen for Android, and Audacity on my PC.
I set the frequency to 3 kHz and recorded the mobile phone moving in a circular motion near the
microphone of the PC. A piece of string was duct-taped to the back a mobile phone. You can also do this
in a linear way by just moving the mobile phone back and forth in your hand.
In Audacity, the Audio Track Spectrogram Settings were configured to a Min Frequency of 2500 Hz and
Max Frequency of 3500 Hz. The Window Size was set to most narrowband (32768). By zooming in on the
frequency axis, the following plot was obtained.
The max frequency observed was 3017 Hz and the min was 2978 Hz. This shows around a 20Hz
increase/decrease in frequency as the mobile phone approached/receded from the laptop.
Rearranging our formula above, where c is now the speed of sound and the phone is our star, we can see
𝑣𝑝ℎ𝑜𝑛𝑒 = 𝑣𝑠𝑜𝑢𝑛𝑑 ∗ (
𝑓𝑠𝑜𝑢𝑟𝑐𝑒
) − 𝑣𝑠𝑜𝑢𝑛𝑑
𝑓𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑
3000
𝑣𝑝ℎ𝑜𝑛𝑒 = 340 ∗ (
) − 340
3020
Giving a phone velocity of around 2ms-1.
Students could check this value using 𝑣 =
2𝜋𝑟
,
𝑇
and measuring the period of motion and radius of orbit of the
phone. The time taken for several orbits and divided by the number of orbits to give a more accurate
figure. Students should think about the uncertainty in the period and the length of string.
Linear motion could also be studied. A larger frequency shift could be achieved moving outside and
strapping the phone to a bicycle.
Students could also experiment with changing the source frequency.
Tom Lyons – June 2017