# Department of Mathematics

## John Scott Russell and the Doppler effect

It is not generally known that John Scott Russell (1808-1882), the discoverer of the soliton, made one of the first experimental observations of what is now known as the Doppler effect, and gave an independent explanation of the theory. The Doppler effect was first described by the Austrian physicist Christian Doppler (1803-1853) in 1842.

Scott Russell's short 1848 report gives no date for his original observation, although he was Editor of the Railway Magazine from 1844 to 1847. The credit for first published account of this effect belongs to the Dutch meteorologist Buys Ballot in 1845.

The following is a short note reprinted from the Report of the Eighteen Meeting of the British Association for the Advancement of Science, 1848, pt. 2, published by John Murray, London in 1849, pp 37-38.

## On Certain Effects produced on Sound by the rapid motion of the observer.

### By J Scott Russell, FRS Ed

Until the production of the very high velocities now given to railway trains, no opportunities have existed of observing any phenomena in which the velocity of the observer has been sufficient to affect the character of sounds. The author having had occasion to make observations on railway trains moving at high velocities, has been led to notice some very curious effects in sounds heard at 50 and 60 miles an hour. These effects are not heard by an observer who is stationary. He found that the sound of the whistle of an engine stationary on the line was heard by a passenger in a rapid train to sound a different note - in a different key from that in which it was heard by the person standing beside it. The same was true of all sounds. The passenger in rapid motion heard them in a different key, which might be either louder or lower in pitch than the true or stationary sound. The explanation of this was given as follows. The pitch of a musical sound is determined by the number of vibrations which reach the ear in a second of time - 32 vibrations per second of an organ-pipe give the note C, and a greater or less number give a more acute sound or one more grave. These vibrations move with a velocity of 1024 feet per second nearly. If an observer in a railway train move at the rate of 56 miles an hour towards a sounding body, he will meet a greater number of undulations in a second of time than if at rest, in the proportion which his movement bears to the velocity of sound; but if he move away from the sounding body he will meet a smaller number in that proportion. In the former case he will hear the sounds a semitone higher, and in the second a semitone lower than the observer at rest. In the case of two trains meeting at this velocity, the one containing the sounding body and the other the observer, the effect is doubled in amount. Before the trains meet the sound is heard two semitones too high, and after they pass two semitones too low - being a difference of a major third. There were next explained the various effects which the noises of a train produced on the ears of passengers at high velocities. The reflected sounds of a train, from surfaces like those of bridges across the line, were at ordinary velocities sent back to the ear changed by less than a tone, so as to cause a harsh discord, which was an element of the unpleasant effect on the ear, of passing a bridge. In a tunnel also the sounds reflected from any irregularities in the front of the train or behind it were discords to the sounds of the train heard directly. He showed however that at speeds of 112 miles an hour these sounds might be those of a harmony with each other and become agreeable, for the sounds reflected in opposite directions would have the interval of a major third.