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Trumpeters on the Steam Train (1845)

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from The Mad Science Book © Reto U. Schneider

 

It could have been a concert organized specially for Dadaists: the locomotive that spent the day of 3 June 1845 shuttling between the towns of Utrecht and Maarssen in Holland was pulling just a single flat-bed truck behind it, on which stood three men. One occupied himself with jotting down figures on a printed form, while another played a G on a trumpet whenever the third man signalled that he should do so.

Standing next to the fireman on the locomotive’s footplate, Christoph Buys Ballot cast nervous glances up at the sky and prayed inwardly that the weather wouldn’t turn. This 28-year-old physicist had been forced to abandon his first attempt to conduct this experiment in February. On that occasion, the musicians were confronted by a blizzard and the cold had put their instruments out of tune. By contrast, this Tuesday was a mild summer’s day, and Buys Ballot stood a good chance of seeing through his experiment. With the help of six trumpet players, two watches and a locomotive, it was designed to test the soundness of a theory that an obscure Austrian professor had devised in 1842 on the colour of stars.

Three years had passed since Buys Ballot had obtained a copy of ‘A Monograph by Mr Doppler’. In this work, which was entitled ‘On the Coloured Light of the Binary Refracted Stars and Other Celestial Bodies’, Christian Doppler postulated that anyone approaching or moving away from a light source at great speed would perceive different colours in it than if he had remained static. This phenomenon could not be observed in everyday life, since it only occurred at high velocities. Nevertheless, Doppler was convinced that anyone seeking to confirm his theory need only look at the stars.

Astronomers had divided the stars that appeared in the night sky into two categories: white stars and coloured stars. White stars were individual stars that appeared not to move, while coloured stars often formed one element of binary stars – that is, two stars orbiting around one another. Doppler believed that the colour of binary stars had to do with the fact that they were alternately moving away from and closer to Earth. The theory that he based on this idea has gone down in the history of physics as the Doppler effect.

Following various disputes concerning the nature of light, physicists in Doppler’s period were broadly in agreement that light radiates like a wave and that the different colours it assumes arise from the different frequencies at which light waves oscillate; thus, violet light oscillates fastest, and red light slowest, while in between, as in a rainbow, came blue, green, yellow and orange. The factor that determines whether a person perceives red or blue is in how rapid a succession the waves of light strike the observer’s eye. Doppler was amazed to discover that nobody hitherto had noticed that motion of the light source or of the observer also played a role in this. A person approaching a light source is moving against the direction of the wave and therefore encounters the waves in quicker succession than if he were standing still. Conversely, anyone moving away from a light source is distancing himself from the wave pulses, which now take longer to catch up with him and thus reach him in slower succession. The same principle also holds good for the opposite case, in which the observer remains static and the light source moves.

Doppler provided a graphic illustration of the principle with the example of a ship steering into the waves and ‘encountering over the same period a greater number of waves and a more violent pounding by them than a ship that either remained motionless or one that was being carried along by the waves and travelling in the same direction as them’.

In his paper, Doppler also calculated the speed at which this effect would become visible to the naked eye – ‘33 miles a second’. This figure effectively discouraged even the most optimistic researcher from trying to demonstrate the Doppler effect in an experiment.

However, as Doppler himself also realized, there was a way round this problem: like light, sound also travels in waves, only much more slowly than light. Accordingly, the postulated effect would ‘also apply absolutely stringently’ to sound waves. Sound is a wave that is composed of rapid and small variations in air pressure, which the human ear is able to register. Just like the ship sailing into the waves, sound-wave pulses reach the ear in quicker succession if a person is moving towards the sound source, and this makes the pitch seem higher than that at which it is being emitted by the source. Doppler calculated that a sound source would have to be approaching the hearer at a velocity of 68 ft per second (70 km/h) in order to change a B into a C, a semitone higher.

Seventy kilometres an hour – now, since the invention of the steam locomotive at the end of the preceding century, this was a speed that could be attained. Buys Ballot approached the director of the Dutch Rhine Railway, who in turn got permission from the country’s interior minister for the ‘free use of a locomotive’. Buys Ballott’s first idea was to use the train’s whistle as his sound source. It was loud and therefore audible over a great distance. Yet from preliminary trials he realized that the note it produced was too impure for a musician to be able to determine its precise pitch. And so Buys Ballot expanded his number of assistants by engaging the services of a handful of the best trumpet players he could find in Utrecht. One of them travelled on the railway car with two assistants while the others waited in three groups along the line at an interval of 400 m (1312 ft) from one another.

On the outward journey, in the service of science, the trumpet player on the railway car would play a G, while the musicians beside the track noted the differences in tone. On the return journey, the roles were reversed: now the trumpet players beside the track played, while the musician on the railway car tried to determine the pitch of the note.

However simple Buys Ballot thought the experiment might be, its actual execution turned out to be far more tricky. In order to achieve the greatest possible difference in tone, the locomotive had to travel as fast as possible, but the faster it went, the more difficult it became to make out the sound of the trumpets above the noise of the engine. Moreover, at this speed, the train was soon far away, meaning that the note was audible only for a very brief instant. On the other hand, if the train went slowly, then the difference in tone was imperceptibly small. Ultimately, Buys Ballot settled on speeds between 18 and 72 kilometres per hour, which he timed with two watches. To his annoyance, however, the fireman could never manage to keep the speeds constant.

Yet Buys Ballot’s main problem was not so much technical as personal: despite being given precise instructions on where to come in, the musicians proved incapable of playing their notes right on cue. Sometimes one of them would forget to play his G, while at others two players would suddenly strike up simultaneously. In Poggendorff’s Annals of Physics and Chemistry, Buys Ballot advised anyone wanting to repeat his experiment to use ‘properly disciplined individuals’.

Once Buys Ballot had repeated the experiments he conducted with valved trumpets on 3 June with louder natural trumpets on 5 June, he was in a position to confirm Doppler’s theory ‘despite some irregularities’. The musicians concurred that the note was higher when the trumpet player was approaching than it was when he was moving away from them. Buys Ballot had a ready explanation as to why this effect was not evident in the noise of a passing coach and horses – as some of the musicians had argued before the experiment. A coach didn’t produce a pure note, but rather a mixture of various high notes. Detecting any shift in tone from this was impossible, even to a musician’s ear.

On similar grounds, Buys Ballot was also convinced that Doppler was mistaken on one point: although his theory was undoubtedly correct, it didn’t account for the colour of the stars. The light emitted by stars was also a mixture, and what is more of diverse colours. If, in line with the Doppler effect, all these simultaneously shifted up a notch, then the lowest-frequency light – i.e. red – would actually have been missing from the spectrum.

Doppler believed that this change in colour was visible in binary stars, but overlooked the fact that stars also emit rays in the invisible infrared part of the spectrum. Infrared light waves are slower still than red ones and are quite simply shifted by the Doppler effect into the visible region. Thus, for all practical purposes, where human visual perception of the phenomenon is concerned, absolutely nothing changes. Ironically, Doppler chose to highlight in the title of his paper precisely that phenomenon – the colour of binary stars – that does not come about as a result of the Doppler effect. Stars actually emit coloured light from the outset.

Nowadays, in all likelihood, Doppler wouldn’t choose the example of binary stars to corroborate his theory, but rather that of ambulances: every child knows that the siren sounds more high-pitched when the ambulance is approaching and more lowpitched when it’s moving away.

Today, countless technical applications in astronomy, chemistry and medicine are based on the Doppler effect. Navigational systems on aircraft rely upon it, the Big Bang Theory could never have been devised without it, and even radar speed traps use it.

Buys Ballot didn’t look that far into the future. The only practical application of the Doppler effect that he envisaged was that it ‘might one day contribute to the manufacture of better musical instruments’.

 


Three years had passed since Buys Ballot had obtained a copy of ‘A Monograph by Mr Doppler’. In this work, which was entitled ‘On the Coloured Light of the Binary Refracted Stars and Other Celestial Bodies’, Christian Doppler postulated that anyone approaching or moving away from a light source at great speed would perceive different colours in it than if he had remained static. This phenomenon could not be observed in everyday life, since it only occurred at high velocities. Nevertheless, Doppler was convinced that anyone seeking to confirm his theory need only look at the stars.

Astronomers had divided the stars that appeared in the night sky into two categories: white stars and coloured stars. White stars were individual stars that appeared not to move, while coloured stars often formed one element of binary stars – that is, two stars orbiting around one another. Doppler believed that the colour of binary stars had to do with the fact that they were alternately moving away from and closer to Earth. The theory that he based on this idea has gone down in the history of physics as the Doppler effect.

Following various disputes concerning the nature of light, physicists in Doppler’s period were broadly in agreement that light radiates like a wave and that the different colours it assumes arise from the different frequencies at which light waves oscillate; thus, violet light oscillates fastest, and red light slowest, while in between, as in a rainbow, came blue, green, yellow and orange. The factor that determines whether a person perceives red or blue is in how rapid a succession the waves of light strike the observer’s eye. Doppler was amazed to discover that nobody hitherto had noticed that motion of the light source or of the observer also played a role in this. A person approaching a light source is moving against the direction of the wave and therefore encounters the waves in quicker succession than if he were standing still. Conversely, anyone moving away from a light source is distancing himself from the wave pulses, which now take longer to catch up with him and thus reach him in slower succession. The same principle also holds good for the opposite case, in which the observer remains static and the light source moves.

Doppler provided a graphic illustration of the principle with the example of a ship steering into the waves and ‘encountering over the same period a greater number of waves and a more violent pounding by them than a ship that either remained motionless or one that was being carried along by the waves and travelling in the same direction as them’.

In his paper, Doppler also calculated the speed at which this effect would become visible to the naked eye – ‘33 miles a second’. This figure effectively discouraged even the most optimistic researcher from trying to demonstrate the Doppler effect in an experiment.

However, as Doppler himself also realized, there was a way round this problem: like light, sound also travels in waves, only much more slowly than light. Accordingly, the postulated effect would ‘also apply absolutely stringently’ to sound waves. Sound is a wave that is composed of rapid and small variations in air pressure, which the human ear is able to register. Just like the ship sailing into the waves, sound-wave pulses reach the ear in quicker succession if a person is moving towards the sound source, and this makes the pitch seem higher than that at which it is being emitted by the source. Doppler calculated that a sound source would have to be approaching the hearer at a velocity of 68 ft per second (70 km/h) in order to change a B into a C, a semitone higher.

Seventy kilometres an hour – now, since the invention of the steam locomotive at the end of the preceding century, this was a speed that could be attained. Buys Ballot approached the director of the Dutch Rhine Railway, who in turn got permission from the country’s interior minister for the ‘free use of a locomotive’. Buys Ballott’s first idea was to use the train’s whistle as his sound source. It was loud and therefore audible over a great distance. Yet from preliminary trials he realized that the note it produced was too impure for a musician to be able to determine its precise pitch. And so Buys Ballot expanded his number of assistants by engaging the services of a handful of the best trumpet players he could find in Utrecht. One of them travelled on the railway car with two assistants while the others waited in three groups along the line at an interval of 400 m (1312 ft) from one another.

On the outward journey, in the service of science, the trumpet player on the railway car would play a G, while the musicians beside the track noted the differences in tone. On the return journey, the roles were reversed: now the trumpet players beside the track played, while the musician on the railway car tried to determine the pitch of the note.

However simple Buys Ballot thought the experiment might be, its actual execution turned out to be far more tricky. In order to achieve the greatest possible difference in tone, the locomotive had to travel as fast as possible, but the faster it went, the more difficult it became to make out the sound of the trumpets above the noise of the engine. Moreover, at this speed, the train was soon far away, meaning that the note was audible only for a very brief instant. On the other hand, if the train went slowly, then the difference in tone was imperceptibly small. Ultimately, Buys Ballot settled on speeds between 18 and 72 kilometres per hour, which he timed with two watches. To his annoyance, however, the fireman could never manage to keep the speeds constant.

Yet Buys Ballot’s main problem was not so much technical as personal: despite being given precise instructions on where to come in, the musicians proved incapable of playing their notes right on cue. Sometimes one of them would forget to play his G, while at others two players would suddenly strike up simultaneously. In Poggendorff’s Annals of Physics and Chemistry, Buys Ballot advised anyone wanting to repeat his experiment to use ‘properly disciplined individuals’.

Once Buys Ballot had repeated the experiments he conducted with valved trumpets on 3 June with louder natural trumpets on 5 June, he was in a position to confirm Doppler’s theory ‘despite some irregularities’. The musicians concurred that the note was higher when the trumpet player was approaching than it was when he was moving away from them. Buys Ballot had a ready explanation as to why this effect was not evident in the noise of a passing coach and horses – as some of the musicians had argued before the experiment. A coach didn’t produce a pure note, but rather a mixture of various high notes. Detecting any shift in tone from this was impossible, even to a musician’s ear.

On similar grounds, Buys Ballot was also convinced that Doppler was mistaken on one point: although his theory was undoubtedly correct, it didn’t account for the colour of the stars. The light emitted by stars was also a mixture, and what is more of diverse colours. If, in line with the Doppler effect, all these simultaneously shifted up a notch, then the lowest-frequency light – i.e. red – would actually have been missing from the spectrum.

Doppler believed that this change in colour was visible in binary stars, but overlooked the fact that stars also emit rays in the invisible infrared part of the spectrum. Infrared light waves are slower still than red ones and are quite simply shifted by the Doppler effect into the visible region. Thus, for all practical purposes, where human visual perception of the phenomenon is concerned, absolutely nothing changes. Ironically, Doppler chose to highlight in the title of his paper precisely that phenomenon – the colour of binary stars – that does not come about as a result of the Doppler effect. Stars actually emit coloured light from the outset.

Nowadays, in all likelihood, Doppler wouldn’t choose the example of binary stars to corroborate his theory, but rather that of ambulances: every child knows that the siren sounds more high-pitched when the ambulance is approaching and more lowpitched when it’s moving away.

Today, countless technical applications in astronomy, chemistry and medicine are based on the Doppler effect. Navigational systems on aircraft rely upon it, the Big Bang Theory could never have been devised without it, and even radar speed traps use it.

Buys Ballot didn’t look that far into the future. The only practical application of the Doppler effect that he envisaged was that it ‘might one day contribute to the manufacture of better musical instruments’.
fffcould have been a concert organized specially for Dadaists: the locomotive that spent the day of 3 June 1845 shuttling between the towns of Utrecht and Maasen in Holland was pulling just a single flat-bed truck behind it, on which stood three men. One occupied himself with jotting down figures on a printed form, while another played a G on a trumpet whenever the third man signalled that he should do so.

Standing next to the fireman on the locomotive’s footplate, Christoph Buys Ballot cast nervous glances up at the sky and prayed inwardly that the weather wouldn’t turn. This 28-year-old physicist had been forced to abandon his first attempt to conduct this experiment in February. On that occasion, the musicians were confronted by a blizzard and the cold had put their instruments out of tune. By contrast, this Tuesday was a mild summer’s day, and Buys Ballot stood a good chance of seeing through his experiment. With the help of six trumpet players, two watches and a locomotive, it was designed to test the soundness of a theory that an obscure Austrian professor had devised in 1842 on the colour of stars.

Three years had passed since Buys Ballot had obtained a copy of ‘A Monograph by Mr Doppler’. In this work, which was entitled ‘On the Coloured Light of the Binary Refracted Stars and Other Celestial Bodies’, Christian Doppler postulated that anyone approaching or moving away from a light source at great speed would perceive different colours in it than if he had remained static. This phenomenon could not be observed in everyday life, since it only occurred at high velocities. Nevertheless, Doppler was convinced that anyone seeking to confirm his theory need only look at the stars.

Astronomers had divided the stars that appeared in the night sky into two categories: white stars and coloured stars. White stars were individual stars that appeared not to move, while coloured stars often formed one element of binary stars – that is, two stars orbiting around one another. Doppler believed that the colour of binary stars had to do with the fact that they were alternately moving away from and closer to Earth. The theory that he based on this idea has gone down in the history of physics as the Doppler effect.

Following various disputes concerning the nature of light, physicists in Doppler’s period were broadly in agreement that light radiates like a wave and that the different colours it assumes arise from the different frequencies at which light waves oscillate; thus, violet light oscillates fastest, and red light slowest, while in between, as in a rainbow, came blue, green, yellow and orange. The factor that determines whether a person perceives red or blue is in how rapid a succession the waves of light strike the observer’s eye. Doppler was amazed to discover that nobody hitherto had noticed that motion of the light source or of the observer also played a role in this. A person approaching a light source is moving against the direction of the wave and therefore encounters the waves in quicker succession than if he were standing still. Conversely, anyone moving away from a light source is distancing himself from the wave pulses, which now take longer to catch up with him and thus reach him in slower succession. The same principle also holds good for the opposite case, in which the observer remains static and the light source moves.

Doppler provided a graphic illustration of the principle with the example of a ship steering into the waves and ‘encountering over the same period a greater number of waves and a more violent pounding by them than a ship that either remained motionless or one that was being carried along by the waves and travelling in the same direction as them’.

In his paper, Doppler also calculated the speed at which this effect would become visible to the naked eye – ‘33 miles a second’. This figure effectively discouraged even the most optimistic researcher from trying to demonstrate the Doppler effect in an experiment.

However, as Doppler himself also realized, there was a way round this problem: like light, sound also travels in waves, only much more slowly than light. Accordingly, the postulated effect would ‘also apply absolutely stringently’ to sound waves. Sound is a wave that is composed of rapid and small variations in air pressure, which the human ear is able to register. Just like the ship sailing into the waves, sound-wave pulses reach the ear in quicker succession if a person is moving towards the sound source, and this makes the pitch seem higher than that at which it is being emitted by the source. Doppler calculated that a sound source would have to be approaching the hearer at a velocity of 68 ft per second (70 km/h) in order to change a B into a C, a semitone higher.

Seventy kilometres an hour – now, since the invention of the steam locomotive at the end of the preceding century, this was a speed that could be attained. Buys Ballot approached the director of the Dutch Rhine Railway, who in turn got permission from the country’s interior minister for the ‘free use of a locomotive’. Buys Ballott’s first idea was to use the train’s whistle as his sound source. It was loud and therefore audible over a great distance. Yet from preliminary trials he realized that the note it produced was too impure for a musician to be able to determine its precise pitch. And so Buys Ballot expanded his number of assistants by engaging the services of a handful of the best trumpet players he could find in Utrecht. One of them travelled on the railway car with two assistants while the others waited in three groups along the line at an interval of 400 m (1312 ft) from one another.

On the outward journey, in the service of science, the trumpet player on the railway car would play a G, while the musicians beside the track noted the differences in tone. On the return journey, the roles were reversed: now the trumpet players beside the track played, while the musician on the railway car tried to determine the pitch of the note.

However simple Buys Ballot thought the experiment might be, its actual execution turned out to be far more tricky. In order to achieve the greatest possible difference in tone, the locomotive had to travel as fast as possible, but the faster it went, the more difficult it became to make out the sound of the trumpets above the noise of the engine. Moreover, at this speed, the train was soon far away, meaning that the note was audible only for a very brief instant. On the other hand, if the train went slowly, then the difference in tone was imperceptibly small. Ultimately, Buys Ballot settled on speeds between 18 and 72 kilometres per hour, which he timed with two watches. To his annoyance, however, the fireman could never manage to keep the speeds constant.

Yet Buys Ballot’s main problem was not so much technical as personal: despite being given precise instructions on where to come in, the musicians proved incapable of playing their notes right on cue. Sometimes one of them would forget to play his G, while at others two players would suddenly strike up simultaneously. In Poggendorff’s Annals of Physics and Chemistry, Buys Ballot advised anyone wanting to repeat his experiment to use ‘properly disciplined individuals’.

Once Buys Ballot had repeated the experiments he conducted with valved trumpets on 3 June with louder natural trumpets on 5 June, he was in a position to confirm Doppler’s theory ‘despite some irregularities’. The musicians concurred that the note was higher when the trumpet player was approaching than it was when he was moving away from them. Buys Ballot had a ready explanation as to why this effect was not evident in the noise of a passing coach and horses – as some of the musicians had argued before the experiment. A coach didn’t produce a pure note, but rather a mixture of various high notes. Detecting any shift in tone from this was impossible, even to a musician’s ear.

On similar grounds, Buys Ballot was also convinced that Doppler was mistaken on one point: although his theory was undoubtedly correct, it didn’t account for the colour of the stars. The light emitted by stars was also a mixture, and what is more of diverse colours. If, in line with the Doppler effect, all these simultaneously shifted up a notch, then the lowest-frequency light – i.e. red – would actually have been missing from the spectrum.

Doppler believed that this change in colour was visible in binary stars, but overlooked the fact that stars also emit rays in the invisible infrared part of the spectrum. Infrared light waves are slower still than red ones and are quite simply shifted by the Doppler effect into the visible region. Thus, for all practical purposes, where human visual perception of the phenomenon is concerned, absolutely nothing changes. Ironically, Doppler chose to highlight in the title of his paper precisely that phenomenon – the colour of binary stars – that does not come about as a result of the Doppler effect. Stars actually emit coloured light from the outset.

Nowadays, in all likelihood, Doppler wouldn’t choose the example of binary stars to corroborate his theory, but rather that of ambulances: every child knows that the siren sounds more high-pitched when the ambulance is approaching and more lowpitched when it’s moving away.

Today, countless technical applications in astronomy, chemistry and medicine are based on the Doppler effect. Navigational systems on aircraft rely upon it, the Big Bang Theory could never have been devised without it, and even radar speed traps use it.

Buys Ballot didn’t look that far into the future. The only practical application of the Doppler effect that he envisaged was that it ‘might one day contribute to the manufacture of better musical instruments’.It could have been a concert organized specially for Dadaists: the locomotive that spent the day of 3 June 1845 shuttling between the towns of Utrecht and Maasen in Holland was pulling just a single flat-bed truck behind it, on which stood three men. One occupied himself with jotting down figures on a printed form, while another played a G on a trumpet whenever the third man signalled that he should do so.

Standing next to the fireman on the locomotive’s footplate, Christoph Buys Ballot cast nervous glances up at the sky and prayed inwardly that the weather wouldn’t turn. This 28-year-old physicist had been forced to abandon his first attempt to conduct this experiment in February. On that occasion, the musicians were confronted by a blizzard and the cold had put their instruments out of tune. By contrast, this Tuesday was a mild summer’s day, and Buys Ballot stood a good chance of seeing through his experiment. With the help of six trumpet players, two watches and a locomotive, it was designed to test the soundness of a theory that an obscure Austrian professor had devised in 1842 on the colour of stars.

Three years had passed since Buys Ballot had obtained a copy of ‘A Monograph by Mr Doppler’. In this work, which was entitled ‘On the Coloured Light of the Binary Refracted Stars and Other Celestial Bodies’, Christian Doppler postulated that anyone approaching or moving away from a light source at great speed would perceive different colours in it than if he had remained static. This phenomenon could not be observed in everyday life, since it only occurred at high velocities. Nevertheless, Doppler was convinced that anyone seeking to confirm his theory need only look at the stars.

Astronomers had divided the stars that appeared in the night sky into two categories: white stars and coloured stars. White stars were individual stars that appeared not to move, while coloured stars often formed one element of binary stars – that is, two stars orbiting around one another. Doppler believed that the colour of binary stars had to do with the fact that they were alternately moving away from and closer to Earth. The theory that he based on this idea has gone down in the history of physics as the Doppler effect.

Following various disputes concerning the nature of light, physicists in Doppler’s period were broadly in agreement that light radiates like a wave and that the different colours it assumes arise from the different frequencies at which light waves oscillate; thus, violet light oscillates fastest, and red light slowest, while in between, as in a rainbow, came blue, green, yellow and orange. The factor that determines whether a person perceives red or blue is in how rapid a succession the waves of light strike the observer’s eye. Doppler was amazed to discover that nobody hitherto had noticed that motion of the light source or of the observer also played a role in this. A person approaching a light source is moving against the direction of the wave and therefore encounters the waves in quicker succession than if he were standing still. Conversely, anyone moving away from a light source is distancing himself from the wave pulses, which now take longer to catch up with him and thus reach him in slower succession. The same principle also holds good for the opposite case, in which the observer remains static and the light source moves.

Doppler provided a graphic illustration of the principle with the example of a ship steering into the waves and ‘encountering over the same period a greater number of waves and a more violent pounding by them than a ship that either remained motionless or one that was being carried along by the waves and travelling in the same direction as them’.

In his paper, Doppler also calculated the speed at which this effect would become visible to the naked eye – ‘33 miles a second’. This figure effectively discouraged even the most optimistic researcher from trying to demonstrate the Doppler effect in an experiment.

However, as Doppler himself also realized, there was a way round this problem: like light, sound also travels in waves, only much more slowly than light. Accordingly, the postulated effect would ‘also apply absolutely stringently’ to sound waves. Sound is a wave that is composed of rapid and small variations in air pressure, which the human ear is able to register. Just like the ship sailing into the waves, sound-wave pulses reach the ear in quicker succession if a person is moving towards the sound source, and this makes the pitch seem higher than that at which it is being emitted by the source. Doppler calculated that a sound source would have to be approaching the hearer at a velocity of 68 ft per second (70 km/h) in order to change a B into a C, a semitone higher.

Seventy kilometres an hour – now, since the invention of the steam locomotive at the end of the preceding century, this was a speed that could be attained. Buys Ballot approached the director of the Dutch Rhine Railway, who in turn got permission from the country’s interior minister for the ‘free use of a locomotive’. Buys Ballott’s first idea was to use the train’s whistle as his sound source. It was loud and therefore audible over a great distance. Yet from preliminary trials he realized that the note it produced was too impure for a musician to be able to determine its precise pitch. And so Buys Ballot expanded his number of assistants by engaging the services of a handful of the best trumpet players he could find in Utrecht. One of them travelled on the railway car with two assistants while the others waited in three groups along the line at an interval of 400 m (1312 ft) from one another.

On the outward journey, in the service of science, the trumpet player on the railway car would play a G, while the musicians beside the track noted the differences in tone. On the return journey, the roles were reversed: now the trumpet players beside the track played, while the musician on the railway car tried to determine the pitch of the note.

However simple Buys Ballot thought the experiment might be, its actual execution turned out to be far more tricky. In order to achieve the greatest possible difference in tone, the locomotive had to travel as fast as possible, but the faster it went, the more difficult it became to make out the sound of the trumpets above the noise of the engine. Moreover, at this speed, the train was soon far away, meaning that the note was audible only for a very brief instant. On the other hand, if the train went slowly, then the difference in tone was imperceptibly small. Ultimately, Buys Ballot settled on speeds between 18 and 72 kilometres per hour, which he timed with two watches. To his annoyance, however, the fireman could never manage to keep the speeds constant.

Yet Buys Ballot’s main problem was not so much technical as personal: despite being given precise instructions on where to come in, the musicians proved incapable of playing their notes right on cue. Sometimes one of them would forget to play his G, while at others two players would suddenly strike up simultaneously. In Poggendorff’s Annals of Physics and Chemistry, Buys Ballot advised anyone wanting to repeat his experiment to use ‘properly disciplined individuals’.

Once Buys Ballot had repeated the experiments he conducted with valved trumpets on 3 June with louder natural trumpets on 5 June, he was in a position to confirm Doppler’s theory ‘despite some irregularities’. The musicians concurred that the note was higher when the trumpet player was approaching than it was when he was moving away from them. Buys Ballot had a ready explanation as to why this effect was not evident in the noise of a passing coach and horses – as some of the musicians had argued before the experiment. A coach didn’t produce a pure note, but rather a mixture of various high notes. Detecting any shift in tone from this was impossible, even to a musician’s ear.

On similar grounds, Buys Ballot was also convinced that Doppler was mistaken on one point: although his theory was undoubtedly correct, it didn’t account for the colour of the stars. The light emitted by stars was also a mixture, and what is more of diverse colours. If, in line with the Doppler effect, all these simultaneously shifted up a notch, then the lowest-frequency light – i.e. red – would actually have been missing from the spectrum.

Doppler believed that this change in colour was visible in binary stars, but overlooked the fact that stars also emit rays in the invisible infrared part of the spectrum. Infrared light waves are slower still than red ones and are quite simply shifted by the Doppler effect into the visible region. Thus, for all practical purposes, where human visual perception of the phenomenon is concerned, absolutely nothing changes. Ironically, Doppler chose to highlight in the title of his paper precisely that phenomenon – the colour of binary stars – that does not come about as a result of the Doppler effect. Stars actually emit coloured light from the outset.

Nowadays, in all likelihood, Doppler wouldn’t choose the example of binary stars to corroborate his theory, but rather that of ambulances: every child knows that the siren sounds more high-pitched when the ambulance is approaching and more lowpitched when it’s moving away.

Today, countless technical applications in astronomy, chemistry and medicine are based on the Doppler effect. Navigational systems on aircraft rely upon it, the Big Bang Theory could never have been devised without it, and even radar speed traps use it.

Buys Ballot didn’t look that far into the future. The only practical application of the Doppler effect that he envisaged was that it ‘might one day contribute to the manufacture of better musical instruments’.