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# Five Doppler Effect Experiments with a Smartphone

Updated: Feb 15

Discovered in 1842, the Doppler effect has established itself as an essential investigation tool in modern science. This article details five activities adapted to different learning levels, to be carried out in class, at home or outdoors, simply using a smartphone or tablet. We will also provide specific advice to optimize their implementation. These practical experiments offer a unique opportunity to grasp the concrete applications of the Doppler effect in our daily lives, as well as its role in more advanced fields such as the detection of exo-planets.

Contents :

## A little history ...

In 1842, Christian Doppler, an Austrian physicist, proposed a new theory: the frequency of a wave (whether sound or light) is affected by the movement of the source relative to the observer. This frequency shift is directly proportional to the speed:

Δf = f.Vmobile/Vwave where Vmobile is the speed of the mobile and Vwave is the speed of the wave.

Initially, Christian Doppler's theory was met with skepticism. However, irrefutable proof was soon provided by the meteorologist Buys-Ballot: in 1845, he organized a spectacular experiment by placing musicians on the platform of a train traveling at a speed of 70 km/h and making them play a constant note. Each person on the train journey was able to notice the change in frequency of the sounds emitted by the orchestra as the train passed in front of them, thus convincing themselves that the Doppler effect was not an illusion.

In developing his theory, Christian Doppler hoped to explain the color variations of stars by the change in their light frequency due to their speed relative to the Earth. We now know that the temperature of stars is the main factor in their coloring. However, there is indeed a relativistic Doppler effect for light, which is an extension of the classic Doppler effect, taking into account the effects of Einstein's special relativity: in special relativity, time expansion and length contraction must be considered. The relativistic Doppler effect can then be described by the following formulas for an object moving away from the source (red Doppler):

Δf = f* [(1+ β)/(1-β)] ½ - f, with β = v/c, v relative speed and c speed of light

Today, the Doppler effect is used in many technologies, such as weather radar, medical imaging, and for control and security. It has proven to be a valuable tool for astronomers, allowing them to understand celestial movements and discover new objects such as exoplanets. From the beginnings in Doppler's laboratory to modern observatories peering into the depths of space, the Doppler effect has shaped our understanding of the universe, providing us with windows into the motion and composition of celestial bodies.

## Why study the Doppler effect with a smartphone

If the study of the Doppler effect for light proves difficult, if not impossible, outside of a laboratory, anyone can very easily set up experiments showing its effect on sound waves. All we will need for these experiments is a sound source and a frequency meter, two instruments that are easily available with a smartphone or tablet.

For the sound source, you can use your phone's speaker, or better, a connected speaker, more robust and compact. It is easier for analysis to work with pure, easily identifiable sounds. The FizziQ application includes a synthesizer which can be found in the Tools menu and which can be connected to an external speaker. To ensure precise measures, we will prefer to use a high frequency, greater than 1000 hertz, but not too high so as not to tire the eardrums. Of course, the sound volume must be adjusted so that it is comfortable for the experimenter.

For frequency measurements, we will use the frequency meter in the FizziQ application. This uses the microphone of the smartphone or tablet. Smartphone microphones are extremely sensitive and analyze sound waves precisely, capturing nearly 44,000 pieces of information per second. These characteristics, combined with the significant computing power of digital tools, make it possible to obtain precise data on the shapes and periods of sound waves. Note that with the FizziQ application you can emit pure sound and at the same time analyze the sounds with the microphone. In the majority of cases we therefore only need two telephones.

FizziQ offers several measures for the frequency of a sound wave: fundamental frequency, which is calculated in FizziQ with a Yin algorithm; the dominant frequency, which is the frequency of greatest intensity in the spectrum and which is calculated by a Fourier series transformation; and the frequency spectrum, which allows complex sounds to be analyzed.

One of the frequent problems encountered when testing the Doppler effect is ambient noise which disrupts the measurements. This is especially true when working outdoors. It is therefore necessary to favor a quiet place such as a dead end or a parking lot, and to work with pure frequencies to facilitate frequency measurements.

On the ground, the temptation to take direct measurements is strong. However, sound measurements are delicate, particularly outdoors and in groups. We therefore recommend making sound recordings during the experiments and analyzing these recordings later, in the laboratory or in the classroom. This approach not only saves time, and helps adjust measurement methods in a quiet environment, but also facilitates the sharing of data between different groups, thus ensuring effective and enriching collaboration.

Finally, for those who live in the city, do not have access to quiet places to carry out the experiments, or do not have the time to go our in the field, they can use sound files present in the sound library of the FizziQ application or available on the internet. This use also has the advantage of being able to make reproducible measurements.

Thanks to modern technology, students, science enthusiasts and teachers have at their disposal powerful tools to address the question of the Doppler effect and its direct and powerful applications. Let us now move on to the experiments that can be carried out to understand this phenomenon and its applications.

## Exhibit the Doppler effect

Our first experiment consists simply of highlighting the concept of the Doppler effect. It could not be easier ! Download the FizziQ application on a smartphone (or any other application giving access to a sound synthesizer). In the Tool tab, we select the Synthesizer and generate a pure sound with a frequency of 1000 hertz. We then wave the smartphone in front of us using large movements from left to right then from right to left. We clearly hear a shift in the sound: from the lowest to the highest when the smartphone gets closer, then more serious when it moves away.

It can be verified that the Doppler effect is also present if the detector moves, rather than the sound source. By shaking the receiving smartphone, we notice frequency shifts in the same way. Finally, we will ensure that if the two smartphones are shaken together but without one moving relative to the other, the Doppler effect is then zero. It is therefore the relative movement of the source in relation to the receiver which creates the Doppler effect.

If you wish, you can carry out a more spectacular experiment: you place a smartphone in a plastic bag and perform rotations at arm's length with the bag. If we place ourselves perpendicular to the axis of rotation, we will clearly hear the difference in frequency when the bag approaches and when it moves away. On the other hand, if we position ourselves exactly a few meters in the axis of rotation, we will not hear a change in frequency because the speed of the smartphone along this axis is zero if the rotation is uniform.

Finally, let's highlight by measuring the change in frequency that we perceive by ear. To do this, we use a second smartphone on which we have also installed the FizziQ application. On this second smartphone, we select the Dominant Frequency in the Microphone instrument, and we can see that the frequency increases when the source moves towards the sensor and decreases when it moves away. We have clearly demonstrated the Doppler effect.

## Doppler measurements from a recording

Studying the Doppler effect has never been easier since the advent of digital tools. Simply download an application that measures frequencies and play a sound file containing a Doppler effect recording on another smartphone or connected speaker. In a few minutes, students can make a first measurement and apply the theoretical formulas learned in class. There are many files available on the internet. The easiest to analyze are those that use a mobile emitting pure sound. If the sound is complex we will use fundamental frequency measurement or a history of the frequency spectrum.

The FizziQ app contains everything you need to study the Doppler effect:

1. The Sounds library in the Tool menu offers the choice of two different Doppler effect sounds: a moving mobile emitting a pure sound of 1000 hertz, and the sound of a sound pendulum.

2. To make frequency measurements we will use the dominant frequency measurement or the fundamental frequency measurement in the Measurements tab. These measurements will be recorded over the necessary period of time.

3. In FizziQ it is possible to do both sound generation and measurement at the same time. we therefore need only one smartphone to do the analysis.

4. The experiment notebook allows you to analyze graphs and data, write text, add photos and share the notebook in PDF. It is also interesting to export the data to Excel.

Thanks to the power of modern digital tools, it is very easy for teachers to put the theory of the Doppler effect into practice in a few minutes after the theoretical course. However, it is even more educational for students to make their own sound file, and it is ultimately simpler to do than you might think...

## Measuring the speed of a cyclist using the Doppler effect

How to carry out a life-size Doppler effect experiment? What precautions should we take? What are the best activities? We will see that even if life-size Doppler effect experiments can sometimes be difficult to carry out, with a little perseverance we can carry out very interesting measurements and the challenge of making these measurements is of great educational interest.

An easy-to-perform experiment uses a bike, a connected speaker and a smartphone. We attach the connected speaker to the front of the bike, and we emit on this speaker a pure sound, for example with a frequency of 1000 hertz, generated by the sound synthesizer of the fizziQ application. The cyclist then rides at a constant speed and passes near an operator who measures the frequency. On FizziQ, we will record the frequency as the bike passes by by pressing the REC button. By measuring the frequency before and after the bicycle passes, we deduce the average frequency and the frequency shift, then the speed of the mobile.

To check the measurements taken, you can also record the GPS speed, either with another smartphone, or using the dual measurement option, Duo mode, an option found in the Tools menu. Be careful to select the frequency as the first instrument because it is this which dictates the acquisition frequency.

How can you carry out this experiment with the maximum chance that your field visit will not be a failure?

1. Favor environments without external noise and use pure sound for the broadcast. A park, a cul-de-sac or a school parking lot could do the trick.

2. Rather than trying to take measurements on site, make an audio recording of the cyclist's passage, an audio file that will be shared and analyzed in class. So everyone can do their own analysis.

3. Make sure the speaker broadcasts in all directions, not directly in front, and pay attention to the volume level that poses a health hazard.

Some students will question whether these measurements are the same as those made by the gendarmerie to measure car speeds. Doppler radar works by emitting radio waves (very low wavelength waves) towards vehicles moving on the road. When these radio waves come into contact with a moving vehicle, they are reflected and return to the radar. By measuring the change in frequency of these reflected waves compared to those emitted, the Doppler effect allows the radar to determine the speed of the targeted vehicle.

## Identification of exo-planets

The first exoplanet was discovered by astronomers Michel Mayor and Didier Queloz in 1995. This breakthrough paved the way for the search for other worlds beyond our own solar system and more than 5,000 new planets have been identified to date . Given their distance, it is impossible to detect them visually but their presence can nevertheless be detected by measurement. There are several methods for detecting exo-planets: the transit method which consists of measuring the decrease in the luminosity of a star when the planet passes in front of it, astrometry which measures the small oscillations of a star but requires very high precision in measurements, and variations in the speed of stars by Doppler effect measurement.

When a planet orbits a star, gravity causes the two bodies to exert mutual attraction. Even though the star is much more massive and seems little influenced by the planet, it actually moves back and forth around a common point, called the center of mass of the system. This tiny stellar swing manifests itself as a regular oscillation, synchronized with the orbit of the planet. This effect, although subtle, causes periodic variations in its speed through space. These variations slightly modify the color (or wavelength) of the light emitted by the star because of the Doppler effect. By observing the star's spectral lines, which are very precise lines in its light spectrum characteristic of certain chemical elements, astronomers can detect these tiny color changes and accurately calculate the star's radial velocity. The magnitude of the shifts also gives indications of the mass of the planet, because a more massive planet will induce a more pronounced movement of the star. Furthermore, by observing the periodicity of this movement, we can deduce the orbital period of the planet, and, by applying the laws of celestial mechanics, such as Kepler's third law and Newton's principles of universal gravitation, scientists can determine key characteristics of the exoplanet, such as its mass and the shape of its orbit.

To understand this phenomenon we can do an experiment on sound rather than light. In this experiment we study the frequency variations of a rotating sound pendulum. We place a smartphone set to measure the fundamental (or dominant) frequency and at a distance of one meter we rotate a pendulum composed of a sound source emitting a pure sound of 1000 hertz. Analyzing the frequency allows us to obtain two pieces of information which will tell us about the diameter of the circle described by the weighing pendulum.

This experiment shows that at a distance we can know valuable information about distant objects, provided that they follow very specific physical laws. Here, we know that the mobile describes a circle and therefore the tangential speed and the period make it possible to deduce the radius of the circle traveled. In the case of exo-planets, it is the knowledge of Newton's laws which will make it possible to deduce the mass and the distance from the star.

To find out more, we can consult TP on the star Pegasus 51: https://faculty.uca.edu/njaustin/PHYS1401/Laboratory/exoPlanet.pdf

## Height measurement by Doppler effect

Can we know the height of a building using the Doppler effect? This question will undoubtedly bring to mind the anecdote about Niels Bohr, then a student, who was asked how to measure the height of a building using a barometer. Faced with this question, the young Bohr imagined a catalog of solutions, some of which were humorous by deliberately omitting the solution his teacher expected and which used the dependence of atmospheric pressure on altitude.

One solution consists of dropping a device generating a sound source from the top of the building and measuring the frequency of the sound at ground level. By Doppler effect, by knowing the frequency of the source we will determine the landing speed, and as we also know the law of gravitation, we can deduce the height of the building.

Indeed h = 1/2.g.T ²   , Vmobile = g.T and on the other hand Δf = f.Vmobile/Vwave

from where h = ( Δf.Vwave /f)² /(2.g)

with h, height of the building, T duration of the fall, Vmobile speed of the object in free fall, g the acceleration of gravity i.e. 9.81 m/s2 and Vwave the speed of sound i.e. 340 m/s.

Of course there is no question of dropping a smartphone from the top of a building but you can experience a height of 2m by placing a cushion to absorb the shock of the falling sound source. This sound source can be a small connected speaker which emits a sound of 1000 hertz for example.

## Doppler effect and acoustic beats

We have seen that we can measure the speed of an object emitting sound by measuring its frequency, but can we also measure this speed if we do not have a frequency meter?

An interesting tool that musicians have used for many centuries to measure small frequency shifts is the acoustic beat phenomenon; concept that we discussed in another article: the acoustic beat . An acoustic beat is a regular variation in sound intensity, easily detectable by ear, that occurs when two pure tones are emitted at the same time with a small shift in frequency. If this offset is less than 20 hertz, we can hear the regular and periodic variations due to interference between the two sound waves. For higher offsets, the phenomenon is highlighted by a sound intensity level which shows the characteristic periodic variations in intensity.

If we now consider a moving mobile emitting a pure sound of a certain frequency f. For a stationary observer the wave is shifted by a frequency Δf due to the Doppler effect. For speeds less than 10 m/s, this variation will be of the order of a few tens of hertz. If at the same time this transmitter emits a sound of the same frequency f, the two waves will interfere and create a beat of frequency Δf which can be measured using the sound level measurement. We therefore have a way to measure the frequency of the Doppler shift, without measuring the frequency of the signal, but by measuring its intensity, the result of the interference of two sound sources of the same frequency, one in motion and the other stationary.

Let's make this montage with a sound pendulum. We attack at the end of a pendulum a sound source of a certain frequency f. We then place a sound source of the same frequency f as that emitted by the sound pendulum next to the lowest point of the pendulum, at rest we will only hear one frequency. But if the pendulum oscillates, due to the Doppler effect the sound emitted by the pendulum will be shifted depending on the speed of the pendulum relative to the sound source, and a beating phenomenon will appear. The frequency of the beat will be maximum when the pendulum passes through its lowest point, and minimum (and zero), at its highest point when the speed is zero. We deduce the maximum speed by Doppler effect Vmax = c/(T*f) with c the speed of sound, T the period of the beat and f the frequency used.

The experiment was carried out with a small speaker connected as a mobile, a frequency of 300 hertz, and the use of a smartphone with FizziQ both as a fixed sound source and as a tool for measuring sound intensity. We found a speed of 2.83 m/s. As it is a pendulum we have a simple way to check this result. Indeed, for a pendulum the maximum speed depends on the height h at which the pendulum is released. By conservation of mechanical energy while neglecting friction, the speed at the lowest point is then Vmax = (2*g*h) ½, with h the height for which the mobile is released. In our example the theoretical speed is Vtheo = 2.8 m/s, therefore a value very close to that which we calculated using the acoustic beat method.

The combination of the Doppler effect and acoustic beats was popularized by Ulysse Delabre who used it to estimate the speed of sound. the details can be found in this video: https://www.canal-u.tv/chaines/univ-bordeaux/les-smartphones/18-les-smartphones-determination-de-la-vitesse-du-son-par

## Conclusion

Exploring the Doppler effect through the use of smartphones offers an educational perspective rich in possibilities. This educational approach allows complex scientific concepts to be approached in a practical and interactive way, while taking advantage of modern technology. Students can develop their understanding of fundamental physics principles while acquiring essential skills in observation, measurement and data analysis. This educational approach, by integrating ubiquitous mobile technology into students' daily lives, also provides a unique opportunity to spark their interest in science and encourage them to consider careers in fields related to science, technology, engineering and mathematics (STEM), but also to open their eyes to the technologies that are used in everyday life.

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