Did you know that you can recreate the groundbreaking experiments of famous scientists using just a smartphone? In this article, we present 12 fascinating experiments designed by legendary figures like Pythagoras, Robert Boyle, and Albert Einstein. These experiments are accessible to everyone and don't require complex equipment apart from a smartphone. Whether you're a student, educator, or curious mind, get ready to dive into the rich history of scientific discovery with just your smartphone!
Table of content
Pythagore and the Music Scale - Galileo's Pendulum- Toricelli and the Foundation of Fluid Dynamics - Newton and the Theory of Gravitation - Leibniz and Energy Conservation - Boyle and Sound Waves - Einstein and the Elevator's Thought Experiment - Doppler and the Dopller effect - Nollet and the Measurement of the Speed of Sound - Young and the Theory of Colors - Delambre and the Measurement of the Meridian - Von Helmholtz and the Resonator
Pythagore and the Music Scale
One day, while walking near a forge, it is said that Pythagoras was struck by the harmonious sounds produced by the hammers hitting the anvil. Intrigued, he noticed that the pitch of the sounds depended on the size and weight of the hammers. He then conducted experiments by suspending different weights on strings and striking them, discovering that specific weight ratios produced harmonious sounds. Pythagoras identified three fundamental musical intervals: the octave (ratio 1:2), the fifth (ratio 2:3), and the fourth (ratio 3:4). These intervals formed the basis of the Pythagorean diatonic scale.
Pythagoras, one of the greatest geniuses of ancient Greece (570-495 BC), was a mathematician, philosopher, musician, and mystic. Founder of the Pythagorean movement, he emphasized mathematics, music, and universal harmony. His contributions include the famous Pythagorean theorem, and his interest in music led him to explore musical intervals and the concept of the "harmony of the spheres."
To conduct an analysis similar to Pythagoras and rediscover his insights, we suggest using the sound synthesizer of the app FizziQ, available for free an Android or iOS store. The goal will be to experimentally determine mix of frequencies that seem harmonious to you. For example, choose a frequency of 600 hertz on the first track, and add a frequency on a second track that seems sounds pleasing to the ear. Are the ratio of these two frequencies the same as those found by Pythagoras? Do Pythagorean intervals sound different from other frequency mix? Analyze these sounds with the application's oscilloscope to understand why they are pleasing to the ear. For more information on sound waves and harmonic chords, you can consult our article : Can you see a sound ?
Galileo's Pendulum
Everyone knows the anecdote about Galileo and the falling weights from the top of the Leaning Tower of Pisa, a structure that is part of the architectural ensemble of the Pisa Cathedral, a masterpiece of Romanesque architecture built between the 11th and 12th centuries. Another lesser-known anecdote takes place inside this cathedral. While he was a medical student at the university, Galileo noticed a hanging lamp swinging during a religious service. Intrigued by the lamp's regular movement, he used his pulse to measure the time between oscillations and found that, regardless of the swing's amplitude, the oscillation period remained remarkably constant. This observation marked the beginning of his experiments with pendulums, significantly contributing to classical physics, notably the precise measurement of time and the development of mechanics theory.
A hundred years later, Christian Huygens would confirm Galileo's hypothesis and model the simple pendulum, showing that the oscillation period depends only on the string's length and gravity. For small oscillations: T = 2π * √(l/g), where T is the period in seconds, l is the string's length in meters, and g is the acceleration due to gravity in meters per second squared.
You can experimentally demonstrate this relationship with a smartphone. Attach a hook to the ceiling and tie a long string with a smartphone at the end, secured in a plastic pouch, then set it swinging. The period can be measured in various ways using the smartphone's sensors, such as measuring acceleration, magnetic field variations relative to a magnet on the floor, or luminosity by placing the smartphone on the floor and using a ball at the pendulum's end to cover the detector. If you have a Newton's cradle, verify the oscillations' regularity by measuring the time between impacts using sound level measurements.
Toricelli and the Foundation of Fluid Dynamics
Evangelista Torricelli (1608-1647) was an Italian mathematician and physicist, primarily known for his invention of the mercury barometer. A student of Galileo Galilei, Torricelli continued his work on atmospheric pressure and fluids, developing fundamental principles of fluid dynamics. At the time, scientists did not understand why water pumps could not lift water above 10 meters. Torricelli hypothesized that the air pressure exerted on the water in the tank counterbalances the water column. To test this idea, he filled a tube with mercury, which is denser than water, and inverted it into a basin of mercury. A column of mercury 76 cm high remained, creating a vacuum in the upper part, and this was equivalent to a 10 m column of water, considering the density of mercury (13.6). This experiment proved the existence of atmospheric pressure and the vacuum, thus laying the foundations of modern meteorology and fluid physics.
Another significant contribution from Torricelli is Torricelli's law, which explains that the velocity of fluid flowing out of an orifice under a reservoir is proportional to the square root of the height of the fluid above the orifice. Torricelli's law states that the velocity vvis given by v=2ghv=2gh, where ggis the acceleration due to gravity and hhis the height of the fluid column. This law derives from the principles of energy conservation and fluid dynamics, illustrating how pressure and height influence flow rate.
To replicate this experiment, you can perform a simple demonstration: choose a water bottle and pierce a hole near its bottom. Then, film the bottle with a smartphone as it empties. This video can be analyzed using kinematic analysis to observe the relationship between the water height and flow velocity.
Newton and the Theory of Gravitation
The discovery of gravity by Isaac Newton is one of the most famous moment in the history of science, often embellished by the anecdote of the apple falling from a tree. Although this story is popular, the true manner in which Newton formulated his theory of universal gravitation is more complex and relies on years of meticulous research and observations. By the mid-1660s, Newton was already deeply engaged in the study of physics and mathematics at the University of Cambridge. When an epidemic of plague forced the university to close in 1665, Newton returned to Woolsthorpe, his hometown. It was during this period of enforced retreat, known as his "annus mirabilis" or "miraculous year," that he began developing his revolutionary ideas in physics.
The famous apple story suggests that Newton was inspired to formulate his theory of gravitation after seeing an apple fall from a tree. According to accounts by William Stukeley, a friend of Newton, and John Conduitt, his son-in-law, Newton told them that the apple incident made him ponder the nature of the force that made the apple fall straight to the ground. However, Newton's real breakthrough was not just realizing that objects fall towards the Earth but generalizing this attraction to understand that all bodies in the universe attract each other. Newton began to think that the same force that made the apple fall was also responsible for keeping the planets in orbit around the Sun. He formulated his law of universal gravitation, which states that every particle of matter in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. These works were published in 1687 in his major work, "Philosophiæ Naturalis Principia Mathematica" (Mathematical Principles of Natural Philosophy), which laid the foundations of classical mechanics.
To better understand gravity, you can drop your smartphone instead of an apple. Such an experiment will quickly allow you to estimate ggby measuring the duration of the fall from a certain height. Of course, ensure the smartphone falls onto a soft surface and measure the height and time of the fall accurately. Follow the activity protocol below that describes the procedure: Estimating g.
Leibniz and Energy Conservation
Gottfried Wilhelm Leibniz (1646-1716) was a German polymath, recognized for his significant contributions to philosophy, mathematics, logic, theology, and the sciences. Born in Leipzig to a family of jurists, Leibniz showed remarkable intelligence and an insatiable curiosity for various fields of knowledge from a young age. A polyglot, he mastered several languages, including Latin, Greek, French, and German, and had a working knowledge of English, Italian, and Dutch. This interest in languages led him to propose ideas for improving human communication efficiency, notably by developing a universal language, or "characteristica universalis," based on a logical system of symbols to represent concepts. He believed this universal language could not only facilitate communication between different peoples but also help resolve philosophical or scientific disputes by clarifying concepts. Despite his efforts and extensive research, he never succeeded in implementing this idea.
Leibniz was not convinced by the Cartesian view that the quantity of motion (the product of mass and velocity) was conserved in collisions. He observed that this theory did not account for all experimental observations, particularly in elastic collisions, where the sum of the products of mass and velocity seemed to vary. To resolve this inconsistency, Leibniz proposed the concept of "vis viva" (living force), which he defined as the product of mass and the square of velocity (mv²). He demonstrated that in an isolated system, the sum of these vis viva was conserved, even if the quantity of motion was not necessarily conserved. This innovative idea laid the foundations for our modern understanding of kinetic energy, highlighting the importance of energy conservation in mechanical phenomena.
Many experiments can be conducted with a smartphone to illustrate energy conservation during collisions. To study this concept effectively, use the kinematics module of the FizziQ application. With a smartphone, film an elastic collision and then an inelastic collision, and study the conservation laws of momentum and energy. On the fizziq.org website, you can find a video that will help you make precise measurements: Collision.
Boyle and sound waves
Robert Boyle (1627-1691), an Irish chemist and physicist, is considered one of the founders of modern chemistry. He is best known for Boyle's Law, which describes the inverse relationship between the pressure and volume of a gas at a constant temperature. His experiments with a vacuum pump demonstrated the importance of atmospheric pressure and laid the foundations of physical chemistry. One of his most famous experiments involved placing a turtle in a vacuum chamber to observe the effects of a vacuum on a living organism. Boyle and his assistant, Robert Hooke, noted that as they removed the air from the chamber, the turtle became increasingly inactive. They quickly reintroduced the air before the turtle suffered any permanent damage, dramatically demonstrating the importance of air for the survival of living beings.
Following this observation, Boyle conducted numerous experiments, notably on the propagation of sound. He demonstrated that sound cannot travel through a vacuum by placing a ringing alarm clock inside a glass bell jar connected to a vacuum pump. As the air was gradually removed from the jar, he observed that the sound of the clock became fainter until it was almost inaudible in a near-vacuum. This experiment proved that sound requires a material medium, such as air, to propagate, confirming that a vacuum is an effective acoustic insulator and illustrating the principles of sound wave transmission.
You can replicate this experiment using a container in which you can reduce atmospheric pressure, such as those used to preserve food, or better yet, a laboratory vacuum bell jar. Place a smartphone emitting a constant sound inside the container, which can also measure atmospheric pressure (Apple smartphones have atmospheric pressure sensors). Outside the jar, measure the sound intensity with another smartphone. As you gradually reduce the pressure in the jar, measure the decrease in sound intensity. You will observe that the sound intensity diminishes logarithmically as the pressure in the jar decreases.
Einstein and the Elevator's Thought Experiment
A thought experiment is a hypothetical scenario used to explore the consequences of a principle or theory without real physical experimentation. It involves reasoning through a problem using only imagination and knowledge of physical laws, without requiring empirical evidence or practical execution. Thought experiments are employed in various fields, including physics, philosophy, mathematics, and ethics, serving as powerful tools to conceptualize ideas, challenge existing notions, and stimulate intellectual exploration. Albert Einstein, one of the most eminent users of thought experiments, widely utilized them to develop his revolutionary theories in physics, particularly the theories of special and general relativity. These experiments allowed him to visualize complex problems and paradoxes in physics that were difficult or impossible to test with the technology of his time.
One of Einstein's most famous thought experiments concerns the theory of general relativity: the elevator experiment. Einstein imagined being inside a closed elevator in deep space, accelerating upward. A ball dropped inside the elevator would appear to fall toward the floor similarly to how it would under Earth's gravity. In contrast, a stationary elevator near a planet would experience a similar effect due to gravity. The essence of this experiment is that, within the confines of the elevator, one cannot distinguish between the effects of gravity and pure acceleration.
To recreate this experiment, place a smartphone on a table and open the Absolute Acceleration instrument in the FizziQ app. You will see the value of 9.80 m/s², corresponding to gravitational acceleration. Next, place a mattress on the floor or use a soft bed, press the record button, and then throw the smartphone so that it describes a parabola and lands on the mattress. After stopping the recording and adding the data to the experiment log, you will observe that during the entire period in the air, the measured acceleration is zero. Although the smartphone is in free fall, causing its vertical speed to vary for an observer on the ground, the smartphone itself perceives no force and is in a state of weightlessness.
This experiment exactly reproduces Einstein's elevator thought experiment. The smartphone is equivalent to an elevator falling with the same acceleration as gravity. Inside the smartphone, the accelerometer cannot detect whether it is in free fall or if gravity is absent. For it, as for a person in the elevator, gravity is equivalent to acceleration.
For more information, you can consult our two articles on the subject: one dedicated to gravity and another explaining how an accelerometer works.
Doppler and the Doppler effect
In 1842, Christian Doppler, an Austrian physicist, proposed a new theory about the shift in frequency of a wave when the source moves relative to the observer. His theory was met with great skepticism by the scientific community, mainly because the means of transportation at that time did not allow for a clear demonstration of what the theory predicted. However, an irrefutable proof of Doppler's theory was provided in 1845 by meteorologist Buys-Ballot. He organized a spectacular experiment by placing musicians on a platform of a train moving at 70 km/h, having them play a constant note. People along the track observed the change in frequency of the sounds emitted by the orchestra as the train passed by, confirming that the Doppler effect was not an illusion.
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, according to the equation: Δf = f * Vmobile / Vonde, where Vmobile is the speed of the mobile and Vonde is the speed of the wave.
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 like exoplanets. From its humble beginnings in Doppler's laboratory to modern observatories scanning the depths of space, the Doppler effect has shaped our understanding of the universe, offering insights into the movement and composition of celestial bodies.
Many experiments can be conducted with a smartphone to highlight and experimentally verify the Doppler law. For this, the smartphone's sound synthesizer can be used to generate sounds and measure the frequency of the sounds with the microphone. These experiments concretely demonstrate the frequency shift observed when the sound source moves relative to the observer. You can find five experiments to conduct on this topic by following this link: https://www.fizziq.org/post/experiment-doppler-effect.
Nollet and the Measurement of the Speed of Sound
Jean-Antoine Nollet (1700-1770), also known as Abbé Nollet, was a renowned French physicist and priest noted for his contributions to the study of electricity and acoustics. Born in Pimprez, Nollet began his career in theology before turning to natural sciences. He became a member of the Académie des Sciences and taught experimental physics at the Collège de Navarre in Paris. Nollet is best known for his work on electricity. He was one of the first to demonstrate the effects of static electricity and popularize electrical experiments across Europe. He invented the electrometer, a device for measuring electrical charge, and conducted public demonstrations that captivated the imagination of his era.
In 1738, the Académie des Sciences tasked Nollet with accurately determining the speed of sound. Utilizing the topography of the Paris basin, Nollet placed a cannon on the Montlhéry tower, with observers stationed on Montmartre hill, 28 kilometers away. At night, they timed the interval between seeing the flash and hearing the "BANG" of the cannon. Since the light from the cannon was perceived almost instantaneously, they measured the time required to hear the sound. Nollet calculated the speed of sound by using the distance and the measured time, reporting a speed of 337.2 meters per second to the Académie des Sciences. This value, very close to the modern measurement (about 343 m/s at 20°C), demonstrated the precision and rigor of his scientific method. His experiment marked a turning point in the study of sound waves and remains a notable example of the practical application of scientific principles.
You can easily replicate this experiment in class or at home with two smartphones equipped with the FizziQ application. Use the application's acoustic chronometers, which measure the time between two sound events. Place the two smartphones side by side and start the chronometers by clapping your hands. Then, move one of the phones at least 5 meters away and clap your hands again near the other phone. The chronometers stop, and the speed of sound can be calculated by dividing the distance by the time difference between the two chronometers. To conduct this experiment, follow this link: measure the speed of sound.
Young and the Theory of Colors
Thomas Young, a British physicist and polymath, is famous for his revolutionary work on color theory and trichromatic vision. In the early 19th century, Young was intrigued by how the human eye perceives colors. In 1801, he proposed that color vision relies on three types of receptors in the eye, each sensitive to one of the three primary colors: red, green, and blue. To test his theory, Young used colored filters and light sources of different wavelengths. He demonstrated that the combination of these three base colors could reproduce all other colors perceptible to the human eye. For instance, combining red and green light produces yellow; combining blue and red light produces magenta; and combining all three produces white.
It took over 150 years for the existence of cells sensitive to three different wavelength ranges (most sensitive to green-yellow, green-blue, and blue – not red, green, and blue) to be confirmed. These cells were identified in 1956 by Gunnar Svaetichin. In 1983, this discovery was validated in human retinas during an experiment conducted by Herbert Dartnall, James Bowmaker, and John Mollon, who obtained microspectrophotometric readings of individual cones in human eyes. This discovery profoundly influenced the science of optics, the understanding of visual perception, and was fundamental to the development of modern technologies such as television and computer screens, which use red, green, and blue pixels to display a full range of colors.
To experimentally replicate Young's experiment with a smartphone, follow these steps: Using the Color instrument in the FizziQ app, aim at a color and add this measurement to the experiment notebook. This measurement will give you the amount of primary colors red, green, and blue that make up the color. Using the Color Synthesizer in the Tools section with the quantities determined by the spectrum, you can then reconstruct this color. Any color can be recomposed from the three primary colors. The three primary colors, mixed, are sufficient to create any color we perceive.
Delambre and the Measurement of the Earth
In 1790, the French National Assembly decided to establish a single measurement system using the Earth as a reference. The meter was then defined as one ten-millionth of the distance from the equator to the North Pole along a meridian. Pierre Méchain and Jean-Baptiste Delambre, astronomers and mathematicians, were tasked with measuring this meridian in 1792 to establish the most precise possible estimate of the distance between Dunkirk and Barcelona.
This led to a seven-year adventure for the two scientists. The revolutionary Terror period made travel perilous, especially with an unusual measuring device, the repeating circle. Delambre often had to deal with suspicious and uncooperative national guards, preventing him from working for an entire year. Méchain, initially more fortunate, faced complications in 1793 when Spain declared war on France. This tense political situation hindered his work and travel. Furthermore, Méchain discovered an anomaly of a few seconds of arc in his measurements, which led him to hide his results for fear of discredit. These logistical, political, and personal challenges seriously complicated the mission of defining the meter as one ten-millionth of the meridian's quarter. In 1799, they finally determined the length of the meter to be 0.513074 toise. Confronted with an anomaly in his measurements, Méchain chose to conceal them. Their work laid the foundation for the modern definition of the meter.
Triangulation is the basic mathematical tool used by the two scientists. It is a geometric method used to determine the precise position of a point by measuring angles from two fixed and known reference points. This process involves creating triangles whose distances between points can be calculated using trigonometry laws. In practice, one starts by measuring a baseline between two fixed points, then measures the angles between this baseline and a third visible point. From these measurements, the distance to the third point can be calculated. By repeating this process, a series of triangles is formed, allowing large areas to be mapped with great precision.
A triangulation exercise can be simply performed using the FizziQ app's theodolite. This exercise allows, for example, to calculate distances that are too great or have obstacles preventing direct measurement. For more information on triangulation with FizziQ, you can watch the video: triangulation with FizziQ.
Von Helmholtz and the Resonator
Hermann von Helmholtz was a renowned German scientist known for his contributions in various fields, including physics, physiology, and psychology. An interesting anecdote about Helmholtz relates to his invention of the Helmholtz resonator, developed to identify different frequencies of sounds produced by various musical instruments.
In his quest to understand how humans perceive sounds, Helmholtz designed a series of spheres of different sizes with narrow openings. These spheres, called Helmholtz resonators, were intended to vibrate in resonance with specific frequencies. Helmholtz used these resonators by placing them near his ear to listen to the sounds produced by different instruments. Each resonator was calibrated to amplify a particular frequency, allowing Helmholtz to precisely analyze the sound spectrum of music.
You can easily construct a Helmholtz resonator using a test tube. By blowing over the top of the tube, a sound is produced whose frequency is unique to the tube's geometry. For a closed tube, the fundamental resonance frequency is: f₀ = c/(4L+1.6D), where L is the tube's length and D is the tube's diameter. Using the FizziQ app's frequency meter, you can verify that the sound's frequency corresponds to the tube's calculated resonance frequency.
Another fun experiment involves measuring the frequency of the "pop" sound when opening a bottle of wine. This frequency depends on the cavity between the liquid and the cork. The theoretical frequency of the sound can also be calculated and verified with the appropriate tools. Try it with the following video: Opening a bottle of wine.
Conclusion
Thanks to technological advances, it is possible to recreate iconic scientific experiments with a simple smartphone. Whether you are a teacher, student, or simply curious, these experiments allow you to delve into the history of science and understand the fundamental principles that have shaped our understanding of the world. By exploring the works of legendary figures like Pythagoras, Galileo, Torricelli, and many others, you will discover how seemingly complex concepts can be studied and understood using accessible modern technologies. These activities not only enrich your scientific understanding but also make learning interactive and engaging. So, grab your smartphone and start your journey through the history of science.
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