Heinrich Hertz
Heinrich Rudolf Hertz
Born
Heinrich Rudolf Hertz

(1857-02-22)22 February 1857
Free and Hanseatic City of Hamburg
Died1 January 1894(1894-01-01) (aged 36)
Bonn, German Empire
Alma materUniversity of Munich
University of Berlin
Known forContact mechanics
Electromagnetic radiation
Emagram
Parabolic antenna
Photoelectric effect
Hertzian cone
Hertzian dipole antenna
Hertzian oscillator
Hertz vector
Hertz–Knudsen equation
Hertz's principle of least curvature
AwardsMatteucci Medal (1888)
Rumford Medal (1890)
Scientific career
FieldsElectromagnetism
Electrical engineering
Contact mechanics
InstitutionsUniversity of Kiel
University of Karlsruhe
University of Bonn
Doctoral advisorHermann von Helmholtz
Doctoral studentsVilhelm Bjerknes
Signature

Heinrich Rudolf Hertz (/hɜːrts/ HURTS; German: [ˈhaɪnʁɪç ˈhɛʁts];[1][2] 22 February 1857 – 1 January 1894) was a German physicist who first conclusively proved the existence of the electromagnetic waves predicted by James Clerk Maxwell's equations of electromagnetism. The unit of frequency, cycle per second, was named the "hertz" in his honor.[3]

Biography

Heinrich Rudolf Hertz was born in 1857 in Hamburg, then a sovereign state of the German Confederation, into a prosperous and cultured Hanseatic family. His father was Gustav Ferdinand Hertz.[4] His mother was Anna Elisabeth Pfefferkorn.[5]

While studying at the Gelehrtenschule des Johanneums in Hamburg, Hertz showed an aptitude for sciences as well as languages, learning Arabic. He studied sciences and engineering in the German cities of Dresden, Munich and Berlin, where he studied under Gustav R. Kirchhoff and Hermann von Helmholtz. In 1880, Hertz obtained his PhD from the University of Berlin, and for the next three years remained for post-doctoral study under Helmholtz, serving as his assistant. In 1883, Hertz took a post as a lecturer in theoretical physics at the University of Kiel. In 1885, Hertz became a full professor at the University of Karlsruhe.[6]

In 1886, Hertz married Elisabeth Doll, the daughter of Max Doll, a lecturer in geometry at Karlsruhe. They had two daughters: Johanna, born on 20 October 1887 and Mathilde, born on 14 January 1891, who went on to become a notable biologist. During this time Hertz conducted his landmark research into electromagnetic waves.[7]

Hertz took a position of Professor of Physics and Director of the Physics Institute in Bonn on 3 April 1889, a position he held until his death. During this time he worked on theoretical mechanics with his work published in the book Die Prinzipien der Mechanik in neuem Zusammenhange dargestellt (The Principles of Mechanics Presented in a New Form), published posthumously in 1894.[8]

Death

In 1892, Hertz was diagnosed with an infection (after a bout of severe migraines) and underwent operations to treat the illness. He died after complications in surgery in attempts to fix his condition that was causing these migraines, which some consider to have been a malignant bone condition.[9] He died at the age of 36 in Bonn, Germany, in 1894, and was buried in the Ohlsdorf Cemetery in Hamburg.[10][11][12]

Hertz's wife, Elisabeth Hertz (née Doll; 1864–1941), did not remarry and he was survived by his daughters, Johanna (1887–1967) and Mathilde (1891–1975). Neither ever married or had children, hence Hertz has no living descendants.[13]

Scientific work

Electromagnetic waves

Hertz's 1887 apparatus for generating and detecting radio waves: a spark-gap transmitter (left) consisting of a dipole antenna with a spark gap (S) powered by high voltage pulses from a Ruhmkorff coil (T), and a receiver (right) consisting of a loop antenna and spark gap.
One of Hertz's radio wave receivers: a loop antenna with an adjustable spark micrometer (bottom).[14]

In 1864 Scottish mathematical physicist James Clerk Maxwell proposed a comprehensive theory of electromagnetism, now called Maxwell's equations. Maxwell's theory predicted that coupled electric and magnetic fields could travel through space as an "electromagnetic wave". Maxwell proposed that light consisted of electromagnetic waves of short wavelength, but no one had been able to prove this, or generate or detect electromagnetic waves of other wavelengths.[15]

During Hertz's studies in 1879 Helmholtz suggested that Hertz's doctoral dissertation be on testing Maxwell's theory. Helmholtz had also proposed the "Berlin Prize" problem that year at the Prussian Academy of Sciences for anyone who could experimentally prove an electromagnetic effect in the polarization and depolarization of insulators, something predicted by Maxwell's theory.[16][17] Helmholtz was sure Hertz was the most likely candidate to win it.[17] Not seeing any way to build an apparatus to experimentally test this, Hertz thought it was too difficult, and worked on electromagnetic induction instead. Hertz did produce an analysis of Maxwell's equations during his time at Kiel, showing they did have more validity than the then prevalent "action at a distance" theories.[18]

In the autumn of 1886, after Hertz received his professorship at Karlsruhe, he was experimenting with a pair of Riess spirals when he noticed that discharging a Leyden jar into one of these coils produced a spark in the other coil. With an idea on how to build an apparatus, Hertz now had a way to proceed with the "Berlin Prize" problem of 1879 on proving Maxwell's theory (although the actual prize had expired uncollected in 1882).[19][20] He used a dipole antenna consisting of two collinear one-meter wires with a spark gap between their inner ends, and zinc spheres attached to the outer ends for capacitance, as a radiator. The antenna was excited by pulses of high voltage of about 30 kilovolts applied between the two sides from a Ruhmkorff coil. He received the waves with a resonant single-loop antenna with a micrometer spark gap between the ends. This experiment produced and received what are now called radio waves in the very high frequency range.

Hertz's first radio transmitter: a capacitance loaded dipole resonator consisting of a pair of one meter copper wires with a 7.5 mm spark gap between them, ending in 30 cm zinc spheres.[14] When an induction coil applied a high voltage between the two sides, sparks across the spark gap created standing waves of radio frequency current in the wires, which radiated radio waves. The frequency of the waves was roughly 50 MHz, about that used in modern television transmitters.

Between 1886 and 1889 Hertz conducted a series of experiments that would prove the effects he was observing were results of Maxwell's predicted electromagnetic waves. Starting in November 1887 with his paper "On Electromagnetic Effects Produced by Electrical Disturbances in Insulators", Hertz sent a series of papers to Helmholtz at the Berlin Academy, including papers in 1888 that showed transverse free space electromagnetic waves traveling at a finite speed over a distance.[20][21] In the apparatus Hertz used, the electric and magnetic fields radiated away from the wires as transverse waves. Hertz had positioned the oscillator about 12 meters from a zinc reflecting plate to produce standing waves. Each wave was about 4 meters long. Using the ring detector, he recorded how the wave's magnitude and component direction varied. Hertz measured Maxwell's waves and demonstrated that the velocity of these waves was equal to the velocity of light. The electric field intensity, polarization and reflection of the waves were also measured by Hertz. These experiments established that light and these waves were both a form of electromagnetic radiation obeying the Maxwell equations.[22]

Hertz's directional spark transmitter (center), a half-wave dipole antenna made of two 13 cm brass rods with spark gap at center (closeup left) powered by a Ruhmkorff coil, on focal line of a 1.2 m x 2 m cylindrical sheet metal parabolic reflector.[23] It radiated a beam of 66 cm waves with frequency of about 450 MHz. Receiver (right) is similar parabolic dipole antenna with micrometer spark gap.
Hertz's demonstration of polarization of radio waves: the receiver does not respond when antennas are perpendicular as shown, but as receiver is rotated the received signal grows stronger (as shown by length of sparks) until it reaches a maximum when dipoles are parallel.[23]
Another demonstration of polarization: waves pass through polarizing filter to the receiver only when the wires are perpendicular to dipoles (A), not when parallel (B).[23]
Demonstration of refraction: radio waves bend when passing through a prism made of pitch, similarly to light waves when passing through a glass prism.[23]
Hertz' plot of standing waves created when radio waves are reflected from a sheet of metal

Hertz did not realize the practical importance of his radio wave experiments. He stated that,[24][25][26]

It's of no use whatsoever ... this is just an experiment that proves Maestro Maxwell was right—we just have these mysterious electromagnetic waves that we cannot see with the naked eye. But they are there.

Asked about the applications of his discoveries, Hertz replied,[24][27]

Nothing, I guess

Hertz's proof of the existence of airborne electromagnetic waves led to an explosion of experimentation with this new form of electromagnetic radiation, which was called "Hertzian waves" until around 1910 when the term "radio waves" became current. Within 10 years researchers such as Oliver Lodge, Ferdinand Braun, and Guglielmo Marconi employed radio waves in the first wireless telegraphy radio communication systems, leading to radio broadcasting, and later television. In 1909, Braun and Marconi received the Nobel Prize in physics for their "contributions to the development of wireless telegraphy".[28] Today radio is an essential technology in global telecommunication networks, and the communications medium used by modern wireless devices.[29][30]

Cathode rays

In 1892, Hertz began experimenting and demonstrated that cathode rays could penetrate very thin metal foil (such as aluminium). Philipp Lenard, a student of Heinrich Hertz, further researched this "ray effect". He developed a version of the cathode tube and studied the penetration by X-rays of various materials. However, Lenard did not realize that he was producing X-rays. Hermann von Helmholtz formulated mathematical equations for X-rays. He postulated a dispersion theory before Röntgen made his discovery and announcement. It was formed on the basis of the electromagnetic theory of light (Wiedmann's Annalen, Vol. XLVIII). However, he did not work with actual X-rays.[31]

Photoelectric effect

Hertz helped establish the photoelectric effect (which was later explained by Albert Einstein) when he noticed that a charged object loses its charge more readily when illuminated by ultraviolet radiation (UV). In 1887, he made observations of the photoelectric effect and of the production and reception of electromagnetic (EM) waves, published in the journal Annalen der Physik. His receiver consisted of a coil with a spark gap, whereby a spark would be seen upon detection of EM waves. He placed the apparatus in a darkened box to see the spark better. He observed that the maximum spark length was reduced when in the box. A glass panel placed between the source of EM waves and the receiver absorbed UV that assisted the electrons in jumping across the gap. When removed, the spark length would increase. He observed no decrease in spark length when he substituted quartz for glass, as quartz does not absorb UV radiation. Hertz concluded his months of investigation and reported the results obtained. He did not further pursue investigation of this effect, nor did he make any attempt at explaining how the observed phenomenon was brought about.[32]

Contact mechanics

Memorial of Heinrich Hertz on the campus of the Karlsruhe Institute of Technology, which translates as At this site, Heinrich Hertz discovered electromagnetic waves in the years 1885–1889.

In 1881 and 1882, Hertz published two articles[33][34][35] on what was to become known as the field of contact mechanics, which proved to be an important basis for later theories in the field. Joseph Valentin Boussinesq published some critically important observations on Hertz's work, nevertheless establishing this work on contact mechanics to be of immense importance. His work basically summarises how two axi-symmetric objects placed in contact will behave under loading, he obtained results based upon the classical theory of elasticity and continuum mechanics. The most significant flaw of his theory was the neglect of any nature of adhesion between the two solids, which proves to be important as the materials composing the solids start to assume high elasticity. It was natural to neglect adhesion at the time, however, as there were no experimental methods of testing for it.[36]

To develop his theory Hertz used his observation of elliptical Newton's rings formed upon placing a glass sphere upon a lens as the basis of assuming that the pressure exerted by the sphere follows an elliptical distribution. He used the formation of Newton's rings again while validating his theory with experiments in calculating the displacement which the sphere has into the lens. Kenneth L. Johnson, K. Kendall and A. D. Roberts (JKR) used this theory as a basis while calculating the theoretical displacement or indentation depth in the presence of adhesion in 1971.[37] Hertz's theory is recovered from their formulation if the adhesion of the materials is assumed to be zero. Similar to this theory, however using different assumptions, B. V. Derjaguin, V. M. Muller and Y. P. Toporov published another theory in 1975, which came to be known as the DMT theory in the research community, which also recovered Hertz's formulations under the assumption of zero adhesion. This DMT theory proved to be premature and needed several revisions before it came to be accepted as another material contact theory in addition to the JKR theory. Both the DMT and the JKR theories form the basis of contact mechanics upon which all transition contact models are based and used in material parameter prediction in nanoindentation and atomic force microscopy. These models are central to the field of tribology and he was named as one of the 23 "Men of Tribology" by Duncan Dowson.[38] Despite preceding his great work on electromagnetism (which he himself considered with his characteristic soberness to be trivial[24]), Hertz's research on contact mechanics has facilitated the age of nanotechnology.

Hertz also described the "Hertzian cone", a type of fracture mode in brittle solids caused by the transmission of stress waves.[39]

Meteorology

Hertz always had a deep interest in meteorology, probably derived from his contacts with Wilhelm von Bezold (who was his professor in a laboratory course at the Munich Polytechnic in the summer of 1878). As an assistant to Helmholtz in Berlin, he contributed a few minor articles in the field, including research on the evaporation of liquids,[40] a new kind of hygrometer, and a graphical means of determining the properties of moist air when subjected to adiabatic changes.[41]

Philosophy of science

In the introduction of his 1894 book Principles of Mechanics, Hertz discusses the different "pictures" used to represent physics in his time including the picture of Newtonian mechanics (based on mass and forces), a second picture (based on energy conservation and Hamilton's principle) and his own picture (based uniquely on space, time, mass and the Hertz principle), comparing them in terms of 'permissibility’, ‘correctness’ and ‘appropriateness’.[42] Hertz wanted to remove "empty assumptions" and argue against the Newtonian concept of force and against action at a distance.[42] Philosopher Ludwig Wittgenstein inspired by Hertz's work, extended his picture theory into a picture theory of language in his 1921 Tractatus Logico-Philosophicus which influenced logical positivism.[42]

Third Reich treatment

Because Hertz's family converted from Judaism to Lutheranism two decades before his birth, his legacy ran afoul of the Nazi government in the 1930s, a regime that classified people by "race" instead of religious affiliation.[43][44]

Hertz's name was removed from streets and institutions and there was even a movement to rename the frequency unit named in his honor (hertz) after Hermann von Helmholtz instead, keeping the symbol (Hz) unchanged.[44]

His family was also persecuted for their non-Aryan status. Hertz's youngest daughter, Mathilde, lost a lectureship at Berlin University after the Nazis came to power and within a few years she, her sister, and their mother left Germany and settled in England.[45]

Legacy and honors

Heinrich Hertz

Heinrich Hertz's nephew Gustav Ludwig Hertz was a Nobel Prize winner, and Gustav's son Carl Helmut Hertz invented medical ultrasonography. His daughter Mathilde Carmen Hertz was a well-known biologist and comparative psychologist. Hertz's grandnephew Hermann Gerhard Hertz, professor at the University of Karlsruhe, was a pioneer of NMR-spectroscopy and in 1995 published Hertz's laboratory notes.[46]

The SI unit hertz (Hz) was established in his honor by the International Electrotechnical Commission in 1930 for frequency, an expression of the number of times that a repeated event occurs per second. It was adopted by the CGPM (Conférence générale des poids et mesures) in 1960, officially replacing the previous name, "cycles per second" (cps).[47]

In 1928 the Heinrich-Hertz Institute for Oscillation Research was founded in Berlin. Today known as the Fraunhofer Institute for Telecommunications, Heinrich Hertz Institute, HHI.

In 1969, in East Germany, a Heinrich Hertz memorial medal[48] was cast.

The IEEE Heinrich Hertz Medal, established in 1987, is "for outstanding achievements in Hertzian waves [...] presented annually to an individual for achievements which are theoretical or experimental in nature".

The Submillimeter Radio Telescope at Mt. Graham, Arizona, constructed in 1992 is named after him.

A crater that lies on the far side of the Moon, just behind the eastern limb, is the Hertz crater, named in his honor.

On his birthday in 2012, Google honored Hertz with a Google doodle, inspired by his life's work, on its home page.[49][50]

Works

  • Ueber die Induction in rotirenden Kugeln (in German). Berlin: Schade. 1880.
  • Die Prinzipien der Mechanik in neuem Zusammenhange dargestellt (in German). Leipzig: Johann Ambrosius Barth. 1894.
  • Schriften vermischten Inhalts (in German). Leipzig: Johann Ambrosius Barth. 1895.

See also

Lists and histories
Electromagnetic radiation
Other

References

  1. ↑ Krech, Eva-Maria; Stock, Eberhard; Hirschfeld, Ursula; Anders, Lutz Christian (2009). Deutsches Aussprachewörterbuch [German Pronunciation Dictionary] (in German). Berlin: Walter de Gruyter. pp. 575, 580. ISBN 978-3-11-018202-6.
  2. ↑ Dudenredaktion; Kleiner, Stefan; Knöbl, Ralf (2015) [First published 1962]. Das Aussprachewörterbuch [The Pronunciation Dictionary] (in German) (7th ed.). Berlin: Dudenverlag. p. 440. ISBN 978-3-411-04067-4.
  3. ↑ IEC History Archived 19 May 2013 at the Wayback Machine. Iec.ch.
  4. ↑ "Biography: Heinrich Rudolf Hertz". MacTutor History of Mathematics archive. Retrieved 2 February 2013.
  5. ↑ Jed Z. Buchwald, The Creation of Scientific Effects - Heinrich Hertz and Electric Waves, University of Chicago Press, 2011, page 45
  6. ↑ Jed Z. Buchwald, The Creation of Scientific Effects - Heinrich Hertz and Electric Waves, University of Chicago Press, 2011, pages 51-65
  7. ↑ Jed Z. Buchwald, The Creation of Scientific Effects - Heinrich Hertz and Electric Waves, University of Chicago Press, 2011, page 218
  8. ↑ Stathis Psillos, Philosophy of Science A-Z, Edinburgh University Press · 2007, page 107
  9. ↑ Robertson, O'Connor. "Heinrich Rudolf Hertz". MacTutor. University of Saint Andrews, Scotland. Retrieved 20 October 2020.
  10. ↑ Hamburger Friedhöfe » Ohlsdorf » Prominente. Friedhof-hamburg.de. Retrieved 22 August 2014.
  11. ↑ Plan Ohlsdorfer Friedhof (Map of Ohlsdorf Cemetery). friedhof-hamburg.de.
  12. ↑ IEEE Institute, Did You Know? Historical ‘Facts’ That Are Not True Archived 10 January 2014 at the Wayback Machine
  13. ↑ Susskind, Charles. (1995). Heinrich Hertz: A Short Life. San Francisco: San Francisco Press. ISBN 0-911302-74-3
  14. 1 2 Appleyard, Rollo (October 1927). "Pioneers of Electrical Communication part 5 – Heinrich Rudolph Hertz" (PDF). Electrical Communication. New York: International Standard Electric Corp. 6 (2): 63–77. Retrieved 19 December 2015.The two images shown are p. 66, fig. 3 and p. 70 fig. 9
  15. ↑ O'Connor, J.J.; Robertson, E.F. (November 1997). "James Clerk Maxwell". School of Mathematical and Computational Sciences University of St Andrews. Archived from the original on 5 November 2021. Retrieved 19 June 2021.
  16. ↑ Heinrich Hertz. nndb.com. Retrieved 22 August 2014.
  17. 1 2 Baird, Davis, Hughes, R.I.G. and Nordmann, Alfred eds. (1998). Heinrich Hertz: Classical Physicist, Modern Philosopher. New York: Springer-Verlag. ISBN 0-7923-4653-X. p. 49
  18. ↑ Heilbron, John L. (2005) The Oxford Guide to the History of Physics and Astronomy. Oxford University Press. ISBN 0195171985. p. 148
  19. ↑ Baird, Davis, Hughes, R.I.G. and Nordmann, Alfred eds. (1998). Heinrich Hertz: Classical Physicist, Modern Philosopher. New York: Springer-Verlag. ISBN 0-7923-4653-X. p. 53
  20. 1 2 Huurdeman, Anton A. (2003) The Worldwide History of Telecommunications. Wiley. ISBN 0471205052. p. 202
  21. ↑ "The most important Experiments – The most important Experiments and their Publication between 1886 and 1889". Fraunhofer Heinrich Hertz Institute. Retrieved 19 February 2016.
  22. ↑ Jed Z. Buchwald, The Creation of Scientific Effects - Heinrich Hertz and Electric Waves, University of Chicago Press, 2011, pages 77-91
  23. 1 2 3 4 Pierce, George Washington (1910). Principles of Wireless Telegraphy. New York: McGraw-Hill Book Co. pp. 51–55.
  24. 1 2 3 "Heinrich Rudolph Hertz". History. Institute of Chemistry, Hebrew Univ. of Jerusalem website. 2004. Archived from the original on 25 September 2009. Retrieved 6 March 2018.{{cite web}}: CS1 maint: bot: original URL status unknown (link)
  25. ↑ Capri, Anton Z. (2007) Quips, quotes, and quanta: an anecdotal history of physics. World Scientific. ISBN 9812709207. p 93.
  26. ↑ Norton, Andrew (2000). Dynamic Fields and Waves. CRC Press. p. 83. ISBN 0750307196.
  27. ↑ Heinrich Hertz (1893). Electric Waves: Being Researches on the Propagation of Electric Action with Finite Velocity Through Space. Dover Publications. ISBN 1-4297-4036-1.
  28. ↑ "The Nobel Prize in Physics 1909". Nobel Foundation. Retrieved 18 January 2019.
  29. ↑ "Heinrich Hertz | German physicist". Encyclopedia Britannica. Retrieved 21 May 2021.
  30. ↑ "How Radio Works". HowStuffWorks. 7 December 2000. Retrieved 14 March 2019.
  31. ↑ Jed Z. Buchwald, The Creation of Scientific Effects - Heinrich Hertz and Electric Waves, University of Chicago Press, 2011, pages 151-153
  32. ↑ Jed Z. Buchwald, The Creation of Scientific Effects - Heinrich Hertz and Electric Waves, University of Chicago Press, 2011, page 244
  33. ↑ Hertz, Heinrich (1882). "Ueber die Berührung fester elastischer Körper". Journal für die reine und angewandte Mathematik. 1882 (92): 156–171. doi:10.1515/crll.1882.92.156. S2CID 123604617.
  34. ↑ Hertz, Heinrich (1882). "Über die Berührung fester elastischer Körper und über die Härte". Verhandlungen des Vereins zur Beförderung des Gewerbefleißes. 1882: 449–463. Retrieved 9 February 2022.
  35. ↑ Hertz, Heinrich (1986). Miscellaneous Papers. London: Macmillan and Co, Ltd. pp. 146–183. Retrieved 13 February 2022.
  36. ↑ Tevis D. B. Jacobs, C. M. Mate, Kevin T. Turner, Robert W Carpick, Understanding the tip-sample contact: An overview of contact mechanics at the nanoscale, November 2013
  37. ↑ Johnson, K. L.; Kendall, K.; Roberts, A. D. (1971). "Surface energy and contact of elastic solids" (PDF). Proceedings of the Royal Society A. 324 (1558): 301–313. Bibcode:1971RSPSA.324..301J. doi:10.1098/rspa.1971.0141. S2CID 137730057.
  38. ↑ Dowson, Duncan (1 April 1979). "Men of Tribology: Heinrich Rudolph Hertz (1857–1894) and Richard Stribeck (1861–1950)". Journal of Lubrication Technology. 101 (2): 115–119. doi:10.1115/1.3453287. ISSN 0022-2305.
  39. ↑ "Purdue University - Study on Hertzian cone crack"
  40. ↑ Hertz, H. (1882). "Ueber die Verdunstung der Flüssigkeiten, insbesondere des Quecksilbers, im luftleeren Raume". Annalen der Physik. 253 (10): 177–193. Bibcode:1882AnP...253..177H. doi:10.1002/andp.18822531002. ISSN 1521-3889.
  41. ↑ Mulligan, J. F.; Hertz, H. G. (1997). "An unpublished lecture by Heinrich Hertz: "On the energy balance of the Earth"". American Journal of Physics. 65 (1): 36–45. Bibcode:1997AmJPh..65...36M. doi:10.1119/1.18565.
  42. 1 2 3 Barker, Peter (2016), "Hertz, Heinrich Rudolf (1857–94)", Routledge Encyclopedia of Philosophy (1 ed.), London: Routledge, doi:10.4324/9780415249126-q046-1, ISBN 978-0-415-25069-6, retrieved 24 August 2023
  43. ↑ Koertge, Noretta. (2007). Dictionary of Scientific Biography. New York: Thomson-Gale. ISBN 0-684-31320-0. Vol. 6, p. 340.
  44. 1 2 Wolff, Stefan L. (2008-01-04) Juden wider Willen – Wie es den Nachkommen des Physikers Heinrich Hertz im NS-Wissenschaftsbetrieb erging. Jüdische Allgemeine.
  45. ↑ MacRakies K. 1993. Surviving the Swastika: Scientific Research in Nazi Germany. New York, USA: Oxford University Press
  46. ↑ Hertz, H.G.; Doncel, M.G. (1995). "Heinrich Hertz's Laboratory Notes of 1887". Archive for History of Exact Sciences. 49 (3): 197–270. doi:10.1007/bf00376092. S2CID 121101068.
  47. ↑ Brian Taylor, H. Gustav Mueller, Fitting and Dispensing Hearing Aids, Plural Publishing, Incorporated · 2020, page 29
  48. ↑ Heinrich Rudolf Hertz Archived 3 June 2013 at the Wayback Machine. Highfields-arc.co.uk. Retrieved 22 August 2014.
  49. ↑ Albanesius, Chloe (22 February 2012). "Google Doodle Honors Heinrich Hertz, Electromagnetic Wave Pioneer". PC Magazine. Retrieved 22 February 2012.
  50. ↑ Heinrich Rudolf Hertz's 155th Birthday. Google (22 February 2012). Retrieved 22 August 2014.

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