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Articles on waves

What are waves? They are a repeated disturbance that spreads out, and transfers energy as it moves forwards.

When we study the physics of waves, we cover these topics:

Simple harmonic motion

Interference and superposition

Waves in 2 dimensions, and refraction

What is sound? How do we hear it?

Actually see the speed of sound at a Queen concert

Sources of sound: String instruments, harmonics, wind instruments, quality of sound

Doppler Effect

Diffraction: The way that waves spread around an obstacle

Resonance: When a vibrating system drives another system to oscillate with greater amplitude at specific frequencies.

MCAS Physics exam: sample wave problems

when time allows we may address these fun related topics:

How do record players and vinyl LPs work?

Anomalous sounds (sound “mirages”?!)

Sonar, echolocation, and ultrasound

Why pianos are never in tune: Math and Physics.

Facts and Fiction of the Schumann Resonance


And in doing so we cover these learning standards:

Massachusetts Science and Technology/Engineering Curriculum Framework

HS-PS4-1. Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling within various media. Recognize that electromagnetic waves can travel through empty space (without a medium) as compared to mechanical waves that require a medium

SAT subject test in Physics: Waves and optics

• General wave properties, such as wave speed, frequency, wavelength, superposition, standing wave diffraction, and Doppler effect
• Reflection and refraction, such as Snell’s law and changes in wavelength and speed
• Ray optics, such as image formation using pinholes, mirrors, and lenses
• Physical optics, such as single-slit diffraction, double-slit interference, polarization, and color


How records work

How record work (private for now)



Facts and Fiction of the Schumann Resonance

Excerpted from Facts and Fiction of the Schumann Resonance, by Brian Dunning,  Skeptoid Podcast #352

It’s increasingly hard to find a web page dedicated to the sales of alternative medicine products or New Age spirituality that does not cite the Schumann resonances as proof that some product or service is rooted in science. … Today we’re going to see what the Schumann resonances actually are, how they formed and what they do, and see if we can determine whether they are, in fact, related to human health.

In physics, Schumann resonances are the name given to the resonant frequency of the Earth’s atmosphere, between the surface and the densest part of the ionosphere.

Schumann Resonance

Image from nasa.gov/mission_pages/sunearth/news/gallery

They’re named for the German physicist Winfried Otto Schumann (1888-1974) who worked briefly in the United States after WWII, and predicted that the Earth’s atmosphere would resonate certain electromagnetic frequencies.

[What is a resonant frequency? Here is a common example. When you blow on a glass bottle at a certain frequency, you can get the bottle to vibrate at the same frequency]

vibrational mode glass beer bottle

from acs.psu.edu/drussell/Demos/BeerBottle/beerbottle.html

This bottle has a resonant frequency of about 196 Hz.

That’s the frequency of sound waves that most efficiently bounce back and forth between the sides of the bottle, at the speed of sound, propagating via the air molecules.

Electromagnetic radiation – like light, and radio waves – is similar, except the waves travel at the speed of light, and do not require a medium like air molecules.

The speed of light is a lot faster than the speed of sound, but the electromagnetic waves have a lot further to go between the ground and the ionosphere than do the sound waves between the sides of the bottle.

This atmospheric electromagnetic resonant frequency is 7.83 Hz, which is near the bottom of the ELF frequency range, or Extremely Low Frequency.

The atmosphere has its own radio equivalent of someone blowing across the top of the bottle: lightning.

Lightning BBC africa thunerstorm plasma

Lightning is constantly flashing all around the world, many times per second; and each bolt is a radio source. This means our atmosphere is continuously resonating with a radio frequency of 7.83 Hz, along with progressively weaker harmonics at 14.3, 20.8, 27.3 and 33.8 Hz.

These are the Schumann resonances. It’s nothing to do with the Earth itself, or with life, or with any spiritual phenomenon; it’s merely an artifact of the physical dimensions of the space between the surface of the Earth and the ionosphere.

Every planet and moon that has an ionosphere has its own set of Schumann resonances defined by the planet’s size.

Jupiter's Galilean moons

Biggest point: this resonated radio from lightning is a vanishingly small component of the electromagnetic spectrum to which we’re all naturally exposed.

The overwhelming source is the sun, blasting the Earth with infrared, visible light, and ultraviolet radiation. All natural sources from outer space, and even radioactive decay of naturally occurring elements on Earth, produce wide-spectrum radio noise. Those resonating in the Schumann cavity are only a tiny, tiny part of the spectrum.

Gamma rays Spectrum Properties NASA

Nevertheless, because the Schumann resonance frequencies are defined by the dimensions of the Earth, many New Age proponents and alternative medicine advocates have come to regard 7.83 Hz as some sort of Mother Earth frequency, asserting the belief that it’s related to life on Earth.

The most pervasive of all the popular fictions surrounding the Schumann resonance is that it is correlated with the health of the human body.


There are a huge number of products and services sold to enhance health or mood, citing the Schumann resonance as the foundational science.

A notable example is the Power Balance bracelets. Tom O’Dowd, formerly the Australian distributor, said that the mylar hologram resonated at 7.83 Hz.

When the bracelet was placed within the body’s natural energy field, the resonance would [supposedly] “reset” your energy field to that frequency.

Well, there were a lot of problems with that claim.

First of all, 7.83 Hz has a wavelength of about 38,000 kilometers. This is about the circumference of the Earth, which is why its atmospheric cavity resonates at that frequency. 38,000 kilometers is WAY bigger than a bracelet! There’s no way that something that tiny could resonate such an enormous wavelength. O’Dowd’s sales pitch was implausible, by a factor of billions, to anyone who understood resonance.

This same fact also applies to the human body. Human beings are so small, relative to a radio wavelength of 38,000 kilometers, that there’s no way our anatomy could detect or interact with such a radio signal in any way.

Proponents of binaural beats cite the Schumann frequency as well. These are audio recordings which combine two slightly offset frequencies to produce a third phantom beat frequency that is perceived from the interference of the two.

Some claim to change your brain’s encephalogram, which they say is a beneficial thing to do. Brain waves range from near zero up to about 100 Hz during normal activity, with a typical reading near the lower end of the scale. This happens to overlap 7.83 — suggesting the aforementioned pseudoscientific connection between humans and the Schumann resonance — but with a critical difference. An audio recording is audio, not radio. It’s the physical oscillation of air molecules, not the propagation of electromagnetic waves. The two have virtually nothing to do with each other.


[Other salespeople claim] that our bodies’ energy fields need to interact with the Schumann resonance, but can’t because of all the interference from modern society [and so they try to sell devices that supposedly connect our body to the Schumann resonance.]

It’s all complete and utter nonsense. Human bodies do not have an energy field: in fact there’s not even any such thing as an energy field. Fields are constructs in which some direction or intensity is measured at every point: gravity, wind, magnetism, some expression of energy. Energy is just a measurement; it doesn’t exist on its own as a cloud or a field or some other entity. The notion that frequencies can interact with the body’s energy field is, as the saying goes, so wrong it’s not even wrong.

Another really common New Age misconception about the Schumann resonance is that it is the resonant frequency of the Earth. But there’s no reason to expect the Earth’s electromagnetic resonant frequency to bear any similarity to the Schumann resonance.

Furthermore, the Earth probably doesn’t even have a resonant electromagnetic frequency. Each of the Earth’s many layers is a very poor conductor of radio; combined all together, the Earth easily absorbs just about every frequency it’s exposed to. If you’ve ever noticed that your car radio cuts out when you drive through a tunnel, you’ve seen an example of this.

Now the Earth does, of course, conduct low-frequency waves of other types. Earthquakes are the prime example of this. The Earth’s various layers propagate seismic waves differently, but all quite well. Seismic waves are shockwaves, a physical oscillation of the medium. Like audio waves, these are unrelated to electromagnetic radio waves.

Each and every major structure within the Earth — such as a mass of rock within a continent, a particular layer of magma, etc. — does have its own resonant frequency for seismic shockwaves, but there is (definitively) no resonant electromagnetic frequency for the Earth as a whole.

So our major point today is that you should be very skeptical of any product that uses the Schumann resonance as part of a sales pitch.

The Earth does not have any particular frequency. Life on Earth is neither dependent upon, nor enhanced by, any specific frequency.

Source:  skeptoid.com/episodes/4352


Resonance: When a vibrating system drives another system to oscillate with greater amplitude at specific frequencies.

from Physicsclassroom.com:

Musical instruments are set into vibrational motion at their natural frequency when a person hits, strikes, strums, plucks or somehow disturbs the object.

Each natural frequency of the object is associated with one of the many standing wave patterns by which that object could vibrate. The natural frequencies of a musical instrument are sometimes referred to as the harmonics of the instrument.

An instrument can be forced into vibrating at one of its harmonics (with one of its standing wave patterns) if another interconnected object pushes it with one of those frequencies. This is known as resonance – when one object vibrating at the same natural frequency of a second object forces that second object into vibrational motion.

Physics Classroom – Sounds – Lesson 5 – Resonance

(work in progress)

RedGrittyBrick, a physicist writing on skeptics.stackexchange.com, notes that a bridge can be susceptible to mechanical resonance:

Mechanical structures usually have one or more frequencies at which some part of the structure oscillates. A tuning fork has a well-defined natural frequency of oscillation. More complex structures may have a dominant natural frequency of oscillation. If some mechanical inputs (such as the pressure of feet walking in unison) have a frequency that is close to a natural frequency of the structure, these inputs will tend to initiate and, over a short time, increase the oscillating movements of the structure. Like pushing a child’s swing at the right time.

One example is London’s Millennium Bridge which was closed shortly after opening because low-frequency vibrations in the bridge were causing large groups of pedestrians to simultaneously shift their weight and reinforcing the oscillation. Dampers were fitted.

London's Millennium Bridge resonance

Skeptics.stackexchange Does a column of marching soldiers have to break their rhythm while crossing a bridge to prevent its collapse?


Related topics

Nikola Tesla and wireless power transmission


Related topics

Facts and Fiction of the Schumann Resonance: On this website


External links

Facts and Fiction of the Schumann Resonance : On Skeptoid

Resonance in AC circuits

Learning Standards

2016 Massachusetts Science and Technology/Engineering Curriculum Framework

HS-PS4-5. Communicate technical information about how some technological devices use the principles of wave behavior and wave interactions with matter to transmit and capture information and energy. Examples of principles of wave behavior include resonance, photoelectric effect, and constructive and destructive interference.


I: adapted from Giancoli Physics

Waves spread as they travel. When waves encounter an obstacle, they bend around it and pass into the region behind it. This phenomenon is called diffraction.
Wave diffraction
The amount of diffraction depends on the λ (wavelength) of the wave and on the size of the obstacle:

Water waves diffraction

(a) λ is much larger than the object. Wave bends around object almost as if it is not there.

(b) and (c) the λ is shorter than the size of the object. There’s more of a “shadow” region behind the obstacle where we might not expect the waves to penetrate — but they do, at least a little.

(d) the obstacle is the same as in part (c) but the λ is longer. More diffraction around object.

Rule: Only when λ is smaller than the size of the object will there be a shadow region.


II. Here we see water waves undergoing diffraction around an island.




Sound waves can diffract in unusual and unexpected ways. See our article on anomalous sounds

Even light itself can diffract!  See our article on light’s wave nature.

Giancoli Physics, Chap 24, The Wave Nature of Light


Real life application: Diffraction in Boston Harbor

spectacle Island Boston Harbor

from bostonfoodandwhine.com

As part of the Central Artery/Tunnel project – the Big Dig – Applied Coastal Research and Engineering did research on wave diffraction in Boston Harbor, around Spectacle Island.

…A detailed beach nourishment design was developed for the southern shoreline of Spectacle Island, which is located within Boston Harbor…  The propagation of waves from Massachusetts Bay into Boston Harbor was modeled using the refraction/diffraction model REF/DIF1. This model predicts the transformation of waves in areas where bathymetry is irregular and where diffraction is important, such as at Spectacle Island. The resulting wave heights, periods, and directions were used as input to both longshore and cross-shore sediment transport models. These models were employed to simulate the performance of several different beach fill designs…

Beach Nourishment Design for Spectacle Island

Spectacle Island Boston Harbor Diffraction

Boston Harbor Islands map

This map is from mass.gov/eea/images/dcr

Learning Standards

2016 Massachusetts Science and Technology/Engineering Curriculum Framework

HS-PS4-1. Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling within various media. Recognize that electromagnetic waves can travel through empty space (without a medium) as compared to mechanical waves that require a medium

SAT subject test in Physics: Waves and optics

• General wave properties, such as wave speed, frequency, wavelength, superposition, standing wave diffraction, and Doppler effect
• Reflection and refraction, such as Snell’s law and changes in wavelength and speed
• Ray optics, such as image formation using pinholes, mirrors, and lenses
• Physical optics, such as single-slit diffraction, double-slit interference, polarization, and color

Anomalous sounds

Here’s an actual news story: “Loud booms heard across Southern New Hampshire: Source of the noise still unclear.”

Nashua police say they don’t know what caused several loud “booms” Saturday afternoon that were heard across Southern New Hampshire. Many reports came from Nashua and surrounding towns, but the sounds were reported as far north as Manchester and as far south as Westford, Massachusetts. Some who heard it in Nashua said they felt their houses shake. Police and fire departments said they have not been alerted to any incidents related to the noise in the area. The cause is still unclear.
– WMUR 9 News. (An ABC affiliated TV station) 2/10/18

How is it possible that such loud, possibly building shaking sounds could be heard in some parts of this town – yet in other parts of the city other residents reported no sound? Also, in a town next door no reports have yet surfaced of anyone hearing them – yet in a town after that, some residents also reported these booming sound.

The answer? It’s complicated, but basically:

(a) there are a wide variety of ways that sounds are produced – including some bizarre ways that most people have never heard of

(b) Sound waves don’t always move in a straight path like many people imagine; changing temperature/density of the air can cause sound waves to bend and diffract, so:

(b1) sound can sometimes travel much further distances than one would expect

(b2) sound can come from a location very different from what “seems obvious” just by listening

(b3) local wind can mask sound, so the same loud sound might be heard in one neighborhood, yet be undetectable by people just a mile away.

Basic physics idea:

Right off the bat, let’s realize that sound doesn’t move in a straight line: It spreads out radially from it’s source, and then – because of a phenomenon known as diffraction – it can even bend around obstacles.

Diffraction of sound Hyperphysics

Source: Hyperphysics, Diffraction of sound, http://hyperphysics.phy-astr.gsu.edu/


“If the air above the earth is warmer than that at the surface, sound will be bent back downward toward the surface by refraction.” – Hyperphysics

sound refraction Hyperphysics 2


Normally, only sound initially directed toward the listener can be heard, but refraction can bend sound downward – effectively amplifying the sound. This can occur over cool lakes.

sound refraction Hyperphysics 3

Sounds also can bounce off of objects, and come to our ears from a direction totally different than the original source.


ABD Engineering writes:

…wind alters sound propagation by the mechanism of refraction; that is, wind bends sound waves. Wind nearer to the ground moves more slowly than wind at higher altitudes, due to surface characteristics such as hills, trees, and man-made structures that interfere with the wind.

This wind gradient, with faster wind at higher elevation and slower wind at lower elevation causes sound waves to bend downward when they are traveling to a location downwind of the source and to bend upward when traveling toward a location upwind of the source.

Waves bending downward means that a listener standing downwind of the source will hear louder noise levels than the listener standing upwind of the source.

Temperature gradients in the atmosphere. On a typical sunny afternoon, air is warmest near the ground and temperature decreases at higher altitudes. This temperature gradient causes sound waves to refract upward, away from the ground and results in lower noise levels being heard at the listener’s position.

In the evening, this temperature gradient will reverse, resulting in cooler temperatures near the ground. This condition, often referred to is a temperature inversion will cause sound to bend downward toward the ground and results in louder noise levels at the listener position.


How Weather Affects an Outdoor Noise Study by ABD Engineering and Design

Cheung Kai-chung, from Physics World (Hong Kong), (Translation by Janny Leung) offers this explanation

Sound wave will be refracted to the ground when traveling with the wind.

Sound waves refracted 1

Sound wave will be refracted upwards when traveling against the wind.

sound waves refracted 2

Source:   Why can a distant sound be heard easier when it travels with the wind? Why does it become weaker if it travels against the wind?

Can wind mask even loud sounds?

A discussion to consider, from Physics forums, includes this phenomenon: “Yes. I have a freeway about 10 blocks South of my house. I can hear the traffic very clearly with no wind, or a South wind. If there is even a slight North wind, the traffic noise becomes almost inaudible. If there is a brisk North wind (over 15 MPH), the sound is completely gone.”



Sound refraction due to cold air:

Also this “…if the air close to the ground is colder than the air above it then sound waves traveling upwards will be bent downwards. This is called Refraction. These refracted sound waves can act to amplify the sound to someone standing far away.”


Sound seems amplified when traveling over water.

In School-for-Champions we read

“If you are sitting in a boat, a sound coming from the shore will seem louder than the same sound heard by a person on land. Sound seems to be amplified when it travels over water. The reason is that the water cools the air above its surface, which then slows down the sound waves near the surface. This causes refraction or bending of the sound wave, such that more sound reaches the boat passenger. Sound waves skimming the surface of the water can add to the amplification effect, if the water is calm.”


See their full lesson here School-for-champions.com: Sound_amplified_over_water

Can snow on the ground affect sound?

“When the ground has a thick layer of fresh, fluffy snow, sound waves are readily absorbed at the surface of the snow. However, the snow surface can become smooth and hard as it ages or if there have been strong winds. Then the snow surface will actually help reflect sound waves. Sounds seem clearer and travel farther under these circumstances.” – Colorado State Climatologist Nolan Doesken

Related topic: The Hum is a phenomenon, or collection of phenomena, involving widespread reports of a persistent and invasive low-frequency humming,rumbling, or droning noise not audible to all people. Hums have been widely reported by national media in the UK and the United States. The Hum is sometimes prefixed with the name of a locality where the problem has been particularly publicized: e.g., the “Bristol Hum” or the “Taos Hum”. It is unclear whether it is a single phenomenon; different causes have been attributed. ”

Human reactions to infrasound – https://en.wikipedia.org/wiki/Infrasound#Human_reactions

Skyquakes or mystery booms are unexplained reports of a phenomenon that sounds like a cannon or a sonic boom coming from the sky. They have been heard in several locations around the world. – https://en.wikipedia.org/wiki/Skyquake

And: The microwave auditory effect, also known as the microwave hearing effect or the Frey effect, consists of audible clicks (or, with speech modulation, spoken words[citation needed]) induced by pulsed/modulated microwave frequencies. The clicks are generated directly inside the human head without the need of any receiving electronic device. The effect was first reported by persons working in the vicinity of radar transponders during World War II. (Wikipedia)

Find  The Guns of Barisal and Anomalous Sound Propagation


Learning Standards


In this topic we are engaging in skeptical analysis of what some term ‘unexplained phenomenon’.

The Massachusetts STEM Curriculum Framework addresses “Understandings about the Nature of Science”

Scientific inquiry is characterized by a common set of values that include: logical thinking, precision, open-mindedness, objectivity, skepticism, replicability of results, and honest and ethical reporting of findings.

Science disciplines share common rules of evidence used to evaluate explanations about
natural systems. Science includes the process of coordinating patterns of evidence with current theory.

Most scientific knowledge is quite durable but is, in principle, subject to change based on new evidence and/or reinterpretation of existing evidence.

The “College Board Standards for College Success: Science” addresses these same skeptical inquiry methods in Standard SP.1: Scientific Questions and Predictions. Asking scientific questions that can be tested empirically and structuring these questions in the form of testable predictions.

Students recognize, formulate, justify and revise scientific questions that can be addressed by science in order to construct explanations.

Students make and justify predictions concerning natural phenomena. Predictions and justifications are based on observations of the world, on knowledge of the discipline and on empirical evidence.

Students determine which data from a specific investigation can be used as evidence to address a scientific question or to support a prediction or an explanation, and distinguish credible data from noncredible data in terms of quality.

Students construct explanations that are based on observations and measurements of the world, on empirical evidence and on reasoning grounded in the theories, principles and concepts of the discipline.

The “Benchmarks for Science Literacy” (AAAS) addresses these same skeptical inquiry methods:

In science, a new theory rarely gains widespread acceptance until its advocates can show that it is borne out by the evidence, is logically consistent with other principles that are not in question, explains more than its rival theories, and has the potential to lead to new knowledge. 12A/H3** (SFAA)

Scientists value evidence that can be verified, hypotheses that can be tested, and theories that can be used to make predictions. 12A/H4** (SFAA)

Curiosity motivates scientists to ask questions about the world around them and seek answers to those questions. Being open to new ideas motivates scientists to consider ideas that they had not previously considered. Skepticism motivates scientists to question and test their own ideas and those that others propose. 12A/H5*

SAT subject test in Physics: Waves and optics

• General wave properties, such as wave speed, frequency, wavelength, superposition, standing wave diffraction, and Doppler effect




Radar was developed secretly for military use by several nations, before and during World War II.The term was coined in 1940 by the United States Navy as an acronym for RAdio Detection And Ranging. It entered English and other languages as a common noun, losing all capitalization.

Radar uses radio waves to determine the range, angle, or velocity of objects.

EM waves can be of many different wavelengths.
Longer wavelengths we perceive as orange and red
Shorter wavelengths are towards the blue end of the spectrum

Fields are at right-angles to each other

They travel through vacuum (empty space) at the speed of light

c  =  speed of light
c  =  3 x 108 m/s       =   186,282 miles/second

So all parts of the EM spectrum – radio, light, Wi-Fi, X-rays,
are all made of exactly the same thing! The only thing different among them? wavelength and frequency!


Our eyes can only see a tiny amount of the EM spectrum.
There are longer and shorter waves as well.

Gamma rays Spectrum Properties NASA

Is  used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain.

A radar system consists of:

transmitter producing electromagnetic radio waves

a receiving antenna (often the same antenna is used for transmitting and receiving)

a receiver and processor to determine properties of the object(s)

Radio waves from the transmitter reflect off the object and return to the receiver

This gives info about the object’s location and speed.


air and terrestrial traffic control

radar astronomy

air-defence systems / antimissile systems


marine radars to locate landmarks and other ships

Commercial marine radar antenna

aircraft anticollision systems

radar by Marshall Brain

outer space surveillance and rendezvous systems

meteorological (weather) precipitation monitoring

Weather radar

flight control systems

guided missile target locating systems

ground-penetrating radar for geological observation

Learning Standards

2016 Massachusetts Science and Technology/Engineering Curriculum Framework

6.MS-PS4-1. Use diagrams of a simple wave to explain that (a) a wave has a repeating pattern with a specific amplitude, frequency, and wavelength, and (b) the amplitude of a wave is related to the energy of the wave.

HS-PS4-1. Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling within various media. Recognize that electromagnetic waves can travel through empty space (without a medium) as compared to mechanical waves that require a medium.

HS-PS4-5. Communicate technical information about how some technological devices use the principles of wave behavior and wave interactions with matter to transmit and capture information and energy. Clarification Statements:
• Emphasis is on qualitative information and descriptions.
• Examples of technological devices could include solar cells capturing light and
converting it to electricity, medical imaging, and communications technology.

Massachusetts Science and Technology/Engineering Curriculum Framework (2006)

6. Electromagnetic Radiation Central Concept: Oscillating electric or magnetic fields can generate electromagnetic waves over a wide spectrum. 6.1 Recognize that electromagnetic waves are transverse waves and travel at the speed of light through a vacuum. 6.2 Describe the electromagnetic spectrum in terms of frequency and wavelength, and identify the locations of radio waves, microwaves, infrared radiation, visible light (red, orange, yellow, green, blue, indigo, and violet), ultraviolet rays, x-rays, and gamma rays on the spectrum.