Echo | Calm Bedtime Reading For Sleep

Drift off with a calm bedtime reading that supports sleep and gently eases insomnia. This calm bedtime reading helps your mind relax as you settle into sleep and let go of the day. Tonight’s episode explores echoes from a scientific perspective, calmly explaining how sound reflects, travels, and returns in a soothing, easy-to-follow way that lets you learn while unwinding.

Benjamin’s steady, calming voice offers gentle, fact-filled narration with no whispering, making this peaceful episode ideal for bedtime listening.

Perfect for insomnia, stress, anxiety, or restless nights, this relaxing science reading gives your thoughts something soft and neutral to focus on as you drift toward sleep. Get comfortable, press play, and allow this gentle exploration of sound to guide you into rest.

Happy sleeping!

Transcript

Welcome to the I Can't Sleep Podcast,

Where I help you drift off one fact at a time.

I'm your host,

Benjamin Boster,

And today's episode is about echoes.

In audio signal processing and acoustics,

An echo is a reflection of sound that arrives at the listener with a delay after the direct sound.

The delay is directly proportional to the distance of the reflecting surface from the source and the listener.

Typical examples are the echo produced by the bottom of a well,

A building,

Or the walls of enclosed and empty rooms.

The word echo derives from the Greek ἔχω,

Itself from ἔχος,

Sound.

Echo in Greek mythology was a mountain nymph whose ability to speak was cursed,

Leaving her able only to repeat the last words spoken to her.

Some animals,

Such as cetaceans,

Dolphins and whales,

And bats,

Use echo for location sensing and navigation,

A process known as echolocation.

Echoes are also the basis of sonar technology.

Walls or other hard surfaces,

Such as mountains and privacy fences,

Reflect acoustic waves.

The reason for reflection may be explained as a discontinuity in the propagation medium.

This can be heard when the reflection returns with sufficient magnitude and delay to be perceived distinctly.

When sound,

Or the echo itself,

Is reflected multiple times from multiple surfaces,

It is characterized as reverberation.

The human ear cannot distinguish echo from the original,

Direct sound,

If the delay is less than 1 tenth of a second.

The speed of sound in dry air is approximately 341 meters per second at a temperature of 25 degrees Celsius.

Therefore,

The reflecting object must be more than 17.

2 meters from the sound source for the echo to be perceived by a person at the source.

When a sound produces an echo in 2 seconds,

The reflecting object is 343 meters away.

In nature,

Canyon walls or rock cliffs facing water are the most common natural settings for hearing echoes.

The echo's strength is frequently measured in Sound Pressure Level,

SPL,

Relative to the directly transmitted wave.

Echoes may be desirable,

As in systems.

In sonar,

Ultrasonic waves are more energetic than audible sounds.

They can travel undeviated through a long distance,

Confined to a narrow beam,

And are not easily absorbed in the medium.

Hence,

Sound ranging and echo depth sounding uses ultrasonic waves.

Ultrasonic waves are sent in all directions from the ship,

And are received at the receiver after the reflection from an obstacle,

Like an enemy ship,

An iceberg,

Or sunken ship.

The distance from the obstacle is found using the formula D equals V times T divided by 2.

Echo depth sounding is a process of finding the depth of the sea,

Using this process.

In the medical field,

Ultrasonic waves of sound are used in ultrasonography and echocardiography.

Electric echo effects have been used since the 1950s in music performance and recording.

The Echoplex is a tape delay effect,

First made in 1959,

That recreates the sound of an acoustic echo.

Designed by Mike Battle,

The Echoplex set a standard for the effect in the 1960s,

And was used by most of the notable guitar players of the era.

Original Echoplexes are highly sought after,

While Echoplexes were used heavily by guitar players,

And the occasional bass player,

Such as Chuck Rainey,

Or trumpeters such as Don Ellis.

Many recording studios also used the Echoplex.

Beginning in the 1970s,

Market built the solid-state Echoplex for Maestro.

In the 2000s,

Most echo effects units used electronic or digital circuitry to recreate the echo effect.

Reflection is the change in direction of a wavefront at an interface between two different media,

So that the wavefront returns into the medium from which it originated.

Common examples include the reflection of light,

Sound,

And water waves.

The law of reflection says that,

For specular reflection,

For example at a mirror,

The angle at which the wave is incident on the surface equals the angle at which it is reflected.

In acoustics,

Reflection causes echoes,

And is used in sonar.

In geology,

It is important in the study of seismic waves.

Reflection is observed with surface waves and bodies of water.

Reflection is observed with many types of electromagnetic wave besides visible light.

Reflection of VHF and higher frequencies is important for radio transmission and for radar.

Even hard X-rays and gamma rays can be reflected at shallow angles with special grazing mirrors.

Reflection of light is either specular,

Mirror-like,

Or diffuse,

Retaining the energy but losing the image,

Depending on the nature of the interface.

In specular reflection,

The phase of the reflected waves depends on the choice of the origin of coordinates.

But the relative phase between S and P,

TE and TM polarizations,

Is fixed by the properties of the media,

And of the interface between them.

A mirror provides the most common model for specular light reflection,

And typically consists of a glass sheet with a metallic coating where the significant reflection occurs.

Reflection is enhanced in metals by suppression of wave propagation beyond their skin depths.

Reflection also occurs at the surface of transparent media,

Such as water or glass,

Although the reflection is generally less effective compared to mirrors.

Reflection of light may occur whenever light travels from a medium of a given refractive index into a medium with a different refractive index.

In the most general case,

A certain fraction of the light is reflected from the interface,

And the remainder is refracted.

Solving Maxwell's equations for a light ray striking a boundary allows the derivation of the Fresnel equations,

Which can be used to predict how much of the light is reflected,

And how much is refracted in a given situation.

This is analogous to the way impedance mismatch in an electric circuit causes reflection of signals.

Total internal reflection of light from a denser medium occurs if the angle of incidence is greater than the critical angle.

Total internal reflection is used as a means of focusing waves that cannot effectively be reflected by common means.

X-ray telescopes are constructed by creating a converging tunnel for the waves.

As the waves interact at low angle with the surface of this tunnel,

They are reflected toward the focus point,

Or toward another interaction with the tunnel surface,

Eventually being directed to the detector at the focus.

A conventional reflector would be useless as the X-rays would simply pass through the intended reflector.

When light reflects off a material with higher refractive index than the medium in which it is traveling,

It undergoes a 180 degree phase shift.

In contrast,

When light reflects off a material with lower refractive index,

The reflected light is in phase with the incident light.

This is an important principle in the field of thin film optics.

Specular reflection forms images.

Reflection from a flat surface forms a mirror image which appears to be reversed from left to right because we compare the image we see to what we would see if we were rotated into the position of the image.

Specular reflection at a curved surface forms an image which may be magnified or demagnified.

Curved mirrors have optical power.

Such mirrors may have surfaces that are spherical or parabolic.

If the reflecting surface is very smooth,

The reflection of light that occurs is called specular or regular reflection.

The laws of reflection are as follows.

1.

The incident ray,

The reflected ray,

And the normal to the reflection surface at the point of the incidence lie in the same plane.

2.

The angle which the incident ray makes with the normal is equal to the angle which the reflected ray makes to the same normal.

3.

The reflected ray and the incident ray are on the opposite sides of the normal.

These three laws can all be derived from the Fresnel equations.

In classical electrodynamics,

Light is considered as an electromagnetic wave,

Which is described by Maxwell's equations.

Light waves incident on a material induce small oscillations of polarization in the individual atoms or oscillation of electrons in metals,

Causing each particle to radiate a small secondary wave in all directions,

Like a dipole antenna.

All these waves add up to give specular reflection and refraction according to the Huygens-Fresnel principle.

In the case of dielectrics such as glass,

The electric field of the light acts on the electrons in the material,

And the moving electrons generate fields and become new radiators.

The refracted light in the glass is the combination of the forward radiation of the electrons and the incident light.

The reflected light is the combination of the backward radiation of all of the electrons.

In metals,

Electrons with no binding energy are called free electrons.

When these electrons oscillate with the incident light,

The phase difference between their radiation field and the incident field is pi radians,

180 degrees.

So the forward radiation cancels the incident light,

And backward radiation is just the reflected light.

Light-matter interaction in terms of photons is a topic of quantum electrodynamics,

And is described in detail by Richard Feynman in his popular book QED,

The Strange Theory of Light and Matter.

When light strikes the surface of a non-metallic material,

It bounces off in all directions due to multiple reflections by the microscopic irregularities inside the material,

E.

G.

The grain boundaries of a polycrystalline material,

Or the cell or fiber boundaries of an organic material,

And by its surface if it is rough.

Thus an image is not formed.

This is called diffuse reflection.

The exact form of the reflection depends on the structure of the material.

One common model for diffuse reflection is Lambertian reflectance,

In which the light is reflected with equal luminance in photometry,

Or radians in radiometry,

In all directions,

As defined by Lambert's cosine law.

The light sent to our eyes by most of the objects we see is due to diffuse reflection from their surface,

So that this is our primary mechanism of physical observation.

Some surfaces exhibit retroreflection.

The structure of these surfaces is such that light is returned in the direction from which it came.

When flying over clouds illuminated by sunlight,

The region seen around the aircraft's shadow will appear brighter,

And a similar effect may be seen from dew on grass.

This partial retroreflection is created by the refractive properties of the curved droplet surface,

And reflective properties at the backside of the droplet.

Some animals' retinas act as retroreflectors,

As this effectively improves the animal's night vision.

Since the lenses of their eyes modify reciprocally the paths of the incoming and outgoing light,

The effect is that the eyes act as a strong retroreflector,

Sometimes seen at night when walking in wildlands with a flashlight.

A simple retroreflector can be made by placing three ordinary mirrors mutually perpendicular to one another,

A corner reflector.

The image produced is the inverse of one produced by a single mirror.

A surface can be made partially retroreflective by depositing a layer of tiny refractive spheres on it,

Or by creating small pyramid-like structures.

In both cases,

Internal reflection causes the light to be reflected back to where it originated.

This is used to make traffic signs,

And automobile license plates reflect light mostly back in the direction from which it came.

In this application,

Perfect retroreflection is not desired,

Since the light would then be directed back into the headlights of an oncoming car,

Rather than to the driver's eyes.

When light reflects off a mirror,

One image appears.

Two mirrors placed exactly face-to-face give the appearance of an infinite number of images along a straight line.

The multiple images seen between two mirrors that sit at an angle to each other lie over a circle.

The center of that circle is located at the imaginary intersection of the mirrors.

A square of four mirrors placed face-to-face give the appearance of an infinite number of images arranged in a plane.

The multiple images seen between four mirrors assembling a pyramid,

In which each pair of mirrors sits at an angle to each other,

Lie over a sphere.

If the base of the pyramid is rectangle-shaped,

The images spread over a section of a torus.

Note that these are theoretical ideals,

Requiring perfect alignment of perfectly smooth,

Perfectly flat,

Perfect reflectors that absorb none of the light.

In practice,

These situations can only be approached,

But not achieved,

Because the effects of any surface imperfections in the reflectors propagate and magnify.

Absorption gradually extinguishes the image,

And any observing equipment,

Biological or technological,

Will interfere.

In this process,

Which is also known as phase conjugation,

Light bounces exactly back in the direction from which it came,

Due to a non-linear optical process.

Not only the direction of the light is reversed,

But the actual wavefronts are reversed as well.

A conjugate reflector can be used to remove aberrations from a beam,

By reflecting it,

And then passing the reflection through the aberrating optics a second time.

If one were to look into a complex conjugation mirror,

It would be black,

Because only the photons which left the pupil would reach the pupil.

Materials that reflect neutrons,

For example beryllium,

Are used in nuclear reactors and nuclear weapons.

In the physical and biological senses,

The reflection of neutrons off atoms within a material is commonly used to determine the material's internal structure.

When a longitudinal sound wave strikes a flat surface,

Sound is reflected in a coherent manner,

Provided that the dimension of the reflective surface is large compared to the wavelength of the sound.

Note that audible sound has a very wide frequency range,

From 20 to about 17,

000 Hz,

And thus a very wide range of wavelengths,

From about 20 mm to 17 m.

As a result,

The overall nature of the reflection varies according to the texture and structure of the surface.

For example,

Porous materials will absorb some energy,

And rough materials,

Where rough is relative to the wavelength,

Tend to reflect in many directions,

To scatter the energy rather than to reflect it coherently.

This leads into the field of architectural acoustics,

Because the nature of these reflections is critical to the auditory feel of a space.

In the theory of exterior noise mitigation,

Reflective surface size mildly detracts from the concept of a noise barrier by reflecting some of the sound in the opposite direction.

Sound reflection can affect the acoustic space.

Seismic waves produced by earthquakes or other sources,

Such as explosions,

May be reflected by layers within the Earth.

Study of the deep reflections of waves generated by earthquakes has allowed seismologists to determine the layered structure of the Earth.

Shallower reflections are used in reflection seismology to study the Earth's crust generally,

And in particular to prospect for petroleum and natural gas deposits.

Scientists have speculated that there could be time reflections.

Scientists from the Advanced Science Research Center at the CUNY Graduate Center report that they observe time reflections by sending broadband signals into a strip of metamaterial filled with electronic switches.

The time reflections in electromagnetic waves are discussed in a 2023 paper published in the journal Nature Physics.

Diffraction is the deviation of waves from straight line propagation without any change in their energy due to an obstacle or through an aperture.

The diffracting object or aperture effectively becomes a secondary source of the propagating wave.

Diffraction is the same physical effect as interference,

But interference is typically applied to superposition of a few waves,

And the term diffraction is used when many waves are superposed.

Italian scientist Francesco Maria Grimaldi coined the word diffraction and was the first to record accurate observations of the phenomenon in 1660.

In classical physics,

The diffraction phenomenon is described by the Huygens-Fresnel principle that treats each point in a propagating wave front as a collection of individual spherical wavelets.

The characteristic pattern is most pronounced when a wave from a coherent source,

Such as a laser,

Encounters a slit or aperture that is comparable in size to its wavelength.

This is due to the addition or interference of different points on the wave front,

Or equivalently each wavelet,

That travel by paths of different lengths to the registering surface.

If there are multiple closely spaced openings,

A complex pattern of varying intensity can result.

These effects also occur when a light wave travels through a medium with a varying refractive index,

Or when a sound wave travels through a medium with varying acoustic impedance.

All waves diffract,

Including gravitational waves,

Water waves,

And other electromagnetic waves,

Such as X-rays and radio waves.

Furthermore,

Quantum mechanics also demonstrates that matter possesses wave-like properties and therefore undergoes diffraction,

Which is measurable at subatomic to molecular levels.

The effects of diffraction of light were first carefully observed and characterized by Francesco Maria Grimaldi,

Who also coined the term diffraction,

From the Latin diffringere,

To break into pieces,

Referring to light breaking up into different directions.

The results of Grimaldi's observations were published posthumously in 1665.

Isaac Newton studied these effects and attributed them to inflection of light rays.

James Gregory,

1638-1675,

Observed the diffraction patterns caused by a bird feather,

Which was effectively the first diffraction grating to be discovered.

Thomas Young developed the first wave treatment of diffraction in 1800.

In his model,

Young proposed that the fringes observed behind an illuminated sharp edge arose from interference between the direct transmitted plane wave and a cylindrical wave that appears to be emitted from the edge.

Augustin-Jean Fresnel revisited the problem and devised an alternative wave theory based on Huygens' principle.

In this model,

Point sources of light are distributed up to the diffraction edge,

But not in the barrier.

These point sources are driven by the incoming plane wave,

And they interfere beyond the barrier.

Fresnel developed a mathematical treatment from his approach,

And Young's model was initially considered incorrect.

Later work showed that Young's more physical approach is equivalent to the Fresnel mathematical one.

In 1818,

Supporters of the corpuscular theory of light proposed that the Paris Academy Prize question addressed diffraction,

Expecting to see the wave theory defeated.

When Fresnel's presentation on his new theory based on wave propagation looked like it might take the prize,

Simeon-Denis Poisson challenged the Fresnel theory by showing that it predicted light in the shadow behind a circular obstruction.

Dominique-François-Jean Largault proceeded to demonstrate experimentally that such light is visible,

Confirming Fresnel's diffraction model.

In 1859,

Hermann von Helmholtz and later in 1882,

Gustav Kirchhoff developed integral equations for diffraction based on the concepts proposed by Fresnel,

As well as approximations needed to apply them.

In general,

All these approaches require formulating the problem in terms of virtual sources.

Cases like absorbing barrier require methods developed in the 1940s based on transverse amplitude diffusion.

Reviews

I was hoping you’d read about yodeling in the Alps in connection with echoes. But a second listen found you went on the reflection, refraction, and defraction. This was a good one, thanks Ben.