On this page
Sound waves travel farther in the sea than light or radar waves can, as NOAA's guide to sonar points out. So how do you find a rock, an iceberg or a submarine you cannot see? During the First World War, the French physicist Paul Langevin worked on an answer: send a narrow beam of ultrasound into the water and listen for the echo. This post covers what his patents describe, why ultrasound was the right choice, a worked example on echo ranging, and what students can learn from how he worked.
Who was Paul Langevin?
Langevin (1872-1946) was a French physicist whose work ranged from the motion of tiny particles to sound under water. In 1908 he presented a short note to the French Academy of Sciences, Sur la théorie du mouvement brownien, on the jittering of particles suspended in a liquid. The Royal Society later published an obituary memoir of him, and in Nature in 1947 J. D. Bernal wrote that his death "was felt as a deep loss, not only to science but also to the cause of peace and social justice throughout the world".
What problem was Langevin trying to solve?
The answer is laid out in a patent he filed with Constantin Chilowsky, a Russian citizen; both were then living in Paris. US patent 1,471,547 was filed on 19 May 1917 and granted in 1923. It lists the things a ship needs to find under water: "mines, submarines, torpedoes, rocks, icebergs, ships in foggy weather".
Older acoustic methods, the patent says, spread sound in all directions, so it weakened quickly and the echo did not show where the obstacle was. Their fix was to vibrate a large surface at an ultrasonic frequency. When the surface is wide compared with the wavelength, the sound stays in a narrow cone. The patent compares the result to "the luminous beam of a searchlight".
It also gives the working numbers: frequencies of 50,000 to 200,000 vibrations per second, wavelengths of 3 to 0.7 centimetres, a speed of sound in water of about 1,500 metres per second, and a transmitting surface 30 to 100 centimetres across. Higher frequencies are absorbed too quickly by the water. Lower ones give beams that are too wide.
Where does quartz come in?
Pierre Curie and his brother Jacques had discovered piezoelectric effects in crystals: some crystals produce a voltage when squeezed, and change shape slightly when a voltage is applied. Langevin turned this into a sound source and a receiver in one. His French patent FR 505,703, filed on 17 September 1918 and published in 1920, is titled (in translation) "Process and apparatus for emitting and receiving underwater elastic waves using the piezoelectric properties of quartz".
Drive a quartz plate with a rapidly alternating voltage and it vibrates, pushing ultrasound into the water. When the echo comes back, the pressure waves squeeze the same crystal and it produces a small voltage you can detect. You can read more about the Curies' discovery in our post on Pierre Curie and piezoelectricity.
Worked example: how far away is the object?
Use the patent's speed of sound in water, v = 1,500 m/s. The echo time below is a sample number for practice.
Wavelength at 50 kHz: λ = v/f = 1,500 / 50,000 = 0.03 m = 3 cm.
Wavelength at 200 kHz: λ = 1,500 / 200,000 = 0.0075 m = 0.75 cm. The patent rounds this to 0.7 cm.
Compare an audible 1 kHz tone: λ = 1,500 / 1,000 = 1.5 m. That is wider than the whole 30 to 100 cm plate, so the sound would spread out instead of forming a beam.
Echo ranging (sample numbers): a pulse returns after t = 0.40 s. The sound travels to the object and back, so the distance is d = vt/2 = 1,500 x 0.40 / 2 = 300 m.
Common mistakes to avoid:
Forgetting to halve. The echo time covers the trip out and back. Without the 2 you get 600 m, twice the real distance.
Using the speed of sound in air. NCERT's Class 11 waves chapter uses 340 m/s for air and 1,486 m/s for water in one exercise. Using the air value would put the object about four times too close.
Mixing kHz and Hz. 50 kHz is 50,000 Hz. Leave out the thousand and your wavelength comes out a thousand times too big.
The speed of sound in the sea is not fixed. NOAA explains that it changes with water temperature and pressure, which bends sound paths, so real sonar has to correct for this.
How is sonar used today?
The principle is the same one Langevin used. NOAA describes active sonar as sending a pulse of sound and timing the echo to work out the range of an object. Scientists use it to chart the seafloor and find shipwrecks. Hospitals use the same echo idea with ultrasound inside the body. The NCERT waves chapter even has an exercise on an ultrasonic scanner that locates tumours, and our post on Ian Donald and the ultrasound scan tells that story.
What can a student take from how Langevin worked?
Start from why the obvious method fails. The patent begins by explaining why ordinary underwater sound was not good enough. Naming the failure pointed to the fix.
Let the numbers choose the design. The frequency range is a trade-off: too high and the water absorbs it, too low and the beam spreads. Good design is often a calculation, not a guess.
Borrow from other fields. The idea joined crystal physics from the Curies with the high-frequency electrical oscillations used in wireless telegraphy, which the patent mentions directly.
Work with others. The first patent carries two names, a physicist and an engineer.
If the link between wavelength, frequency and beam width still feels abstract, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read.
Next step: redo the worked example for a 120 kHz signal and a 0.25 s echo, and check that you get a wavelength of 1.25 cm and a distance of 187.5 m.
