Christian Doppler was born on November 29, 1803 in Salzburg Austria to Johann and Theresa Doppler. Growing up, Doppler had planned on going into the family stonemason business. However, he had chronic health problems that made it impossible to do such physically taxing work (he eventually would die from a pulmonary disease likely caused from the environment in the stonemasonry shop). In 1816 at the age of 13, his father sent him to the “German School” where he won a medal for outstanding scholastic ability. In 1822 he consulted a math professor who recommended that Doppler pursue mathematics at a higher level. So, Doppler decided to study at the Polytechnic Institute in Vienna. After a two and a half years at the school, Doppler decided that he did not like the education system there and he continued to privately study mathematics with a tutor. After finishing his secondary education when he was 21, Doppler worked as a math tutor and began writing essays.
In 1825, Doppler applied for an assistantship at the Polytechnic Institute in Vienna and was rejected. He again applied in 1829 and was this time accepted. In 1833, Doppler’s assistantship had finished and he couldn’t find work at any other universities. He began giving up hope, and planned to move to America to look for work. He had already sold his belongings to finance the trip when he was offered a position as a Professor of Elementary Mathematics and Commercial Accounting at the State Secondary School in Prague. He began making a good salary, married Mathilde Sturmand and began his family.
In 1840 Doppler was elected as an associate to the Royal Bohemian Society of Sciences, and in 1842 he presented his essay “On the Coloured Light of the Double Stars and Certain Other Stars of the Heavens”. This was the foundation of what is now known as the Doppler effect. At the time, Doppler did not know how much of an impact the Doppler effect would have on the world. Christian Doppler’s work in wave physics (sound and optical) has led to advancements in a variety of modern technologies used every day today.
During Doppler’s lifetime, it was well known that the pitch of a sound would vary if the object was moving relative to a listener. Mainly, this was noticed with train whistles when they would increase in pitch when they got closer, and decrease as the train went away. In order to measure this effect, Doppler created a strange experiment. He hired a group of trumpeters to play from a moving train car. He then had musicians with nearly perfect pitch recognition listen to the trumpets as the train traveled towards and away from them. The changes in pitch were noted for the different conditions, and this experiment paved the way for the physics of what is now known as the Doppler Effect. Although the Doppler Effect was originally observed for sound, it eventually was found to hold true for light and all forms of electromagnetic radiation as well.
As we know, the Doppler Effect occurs when a wave-emitting object (or the observer) is moving. If the object is moving towards an observer, the waves will be “crammed” together so that the wavelength will appear to be smaller to the observer. Conversely, if the object is moving away from the observer, the waves will be “pulled” apart and the observed wavelength will be shorter (see figure below).
In the figure to the left, the source is moving right. This causes the wavelength on the right side of the source to be shorter, and the wavelength on the left becomes longer then the short wavelength. In the case of light, an observer on the left would see color shifted towards the red end of the spectrum, and an observer on the right would see color shifted towards the blue end of the spectrum. These effects are known as a “red shift” and a “blue shift,” respectively.
The amount that the frequency is Doppler shifted can be explained mathematically. The math for the cases of sound and electromagnetic radiation are different because when dealing with light or other electromagnetic radiation, relativistic effects must be taken into account since objects do not follow classical physics when they are traveling at extremely high speeds. Therefore, a Lorentz Transformation must be used to modify the equation. The following equations represent the observed frequecy for an emitter moving at velocity, v. The first equation is for sound, and the second is for electromagnetic radiation (including light).
Example: A source is emitting light with a wavelength of 550 nanometers (frequency = c/wavelength = 5.45*10^14 Hz). The source is moving towards an observer with a velocity equal to half the speed of light (c = 2.99*10^9 m/s). What is the observed wavelength?
Solution: Observed Frequency = (5.45*10^14 Hz)*sqrt[(1 + 0.5c/c)/(1 - .5c/c)] = 9.44*10^14 Hz = 318 nm In this case, the observed wavelength is shifted to be 232 nanometers shorter.
The most widely used application of the Doppler effect is radar. By reflecting a signal off of an object, one can tell how fast it is moving and in what direction by measuring frequency shifts and using the math laid out by the Doppler Effect. Radar works by sending out an electromagnetic signal, and measuring the signal that is reflected back by the object it is tracking. Using computers, the Doppler shift of the returned signal can be quickly calculated and the location and velocity of the object can be tracked.
This technology is used in a variety of applications ranging from navigation to storm tracking to speed enforcement. The Doppler effect is also used to study the universe. By measuring the color of a body in space and comparing it to different colors, one can tell if it is moving away or toward the observer. For example, this technique has been used to identify binary star systems and to prove that the universe is expanding.