CONCEPTUAL PHYSICS: UNIT 4

WAVES, LIGHT, AND SOUND

SP4. Students will analyze the properties and applications of waves.

a. Explain the processes that results in the production and energy transfer of electromagnetic waves.

b. Experimentally determine the behavior of waves in various media in terms of reflection, refraction,

and diffraction of waves.

c. Explain the relationship between the phenomena of interference and the principle of superposition.

d. Demonstrate the transfer of energy through different mediums by mechanical waves.

e. Determine the location and nature of images formed by the reflection or refraction of light.

Part 1: Properties of Waves

A vibration is a repetitive back-and-forth motion around a fixed position. Vibration is one form of

kinetic energy. Vibrations are transferred through matter by pulses of energy or by waves. A pulse is a

single disturbance or ripple that moves outward from the point of disturbance. Waves can move as a

single pulse or as a continuous series, carrying energy away from its source.

A wave is a traveling disturbance that carries energy from one location to another. Waves carry energy

away from the source of the disturbance, waves spread the energy outward away from the source of the

disturbance. There are two classes of waves: Mechanical Waves and Electromagnetic Waves.

Electromagnetic waves are the waves that form when light is emitted from a source. Electromagnetic

waves will be discussed later.

Mechanical waves are waves that must pass through matter. Mechanical waves propagate, or travel,

through solids, fluids, or gases. Mechanical waves cannot move through a vacuum, such as in space.

As a mechanical wave passes through matter, the matter is temporarily deformed by the wave energy.

There are two types of mechanical waves: Longitudinal Waves and Transverse Waves. A standing

wave is a special type of mechanical wave.

A longitudinal wave is a compression wave. As the wave moves through the medium, the molecules in

the medium are temporarily compressed and expanded by the wave—molecules are bunched up then

pulled apart. The direction of the wave’s energy is in the same direction as the wave moves. The

regions of the medium where molecules are temporarily compressed are called compressions or

condensations. The regions of the medium where molecules are temporarily expanded are called

rarefactions. Sound waves are examples of longitudinal waves. Sound travels through air (gas), water

(liquid), and walls (solids), but sound cannot travel through space because space is a vacuum.

Longitudinal Wave

Transverse Wave

A transverse wave is a sinusoidal wave. Transverse mechanical waves cause the molecules in the

medium to move up-and-down as the wave passes. The direction of the wave’s energy is perpendicular

to the direction as the wave moves. The regions of the transverse wave where the molecules are pushed

up relative to the equilibrium position are called crests. The regions of the transverse wave where the

molecules are pushed down relative to the equilibrium position are called troughs. Transverse waves are

mechanical waves, and also must pass through a medium. They cannot pass through a vacuum.

A standing wave is a vibration that is produced by a taut string or wire that vibrates back and forth with

a high frequency. Standing waves produce the sound in stringed instruments and pianos.

All mechanical waves produce work. As the wave passes through the matter, the energy of the wave

causes matter to move. Thus longitudinal waves, transverse waves, and standing waves perform

work—work against resistance and mechanical work by pushing and pulling the molecules in the

medium through which they pass.

Frequency and Period

An oscillation or vibration is a repetitive back-and-forth motion. One cycle is defined as one complete

back-and-forth motion of a vibration or of a wave. The time it takes to complete one cycle (one wave or

one vibration) is called the period. The frequency of a wave is defined as the number of waves, cycles,

or vibrations per second. Frequency is reported in units of Hertz, abbreviated Hz. A Hertz is a number

per second, (units of s in the denominator). Period is calculated as the reciprocal of frequency. Period is

reported in units of seconds.

Frequency: t

wavesf

# or

t

cyclesf

# or

t

vibrationsf

#

Period: f

T1

The relationship between frequency and period:

The greater the frequency (more waves, vibrations, or cycles per second), the shorter the period.

The lower the frequency (less waves, vibrations, or cycles per second), the longer the period.

The relationship between frequency and the energy of the wave or vibration

The greater the frequency, the greater the energy (more kinetic energy and more heat)

The lower the frequency, the lower the energy (lesser kinetic energy and lesser heat)

Amplitude and Equilibrium Position

f = frequency (Hz)

t = time (s)

T = Period (s)

Standing Wave

Amplitude is the maximum displacement of the wave from its equilibrium position. The equilibrium

position is the “rest” position of the molecules if the wave was not passing through the medium. The

equilibrium position is the mid-point position around which the vibration or wave moves.

For example, the dashed line of the standing wave represents the equilibrium position of the plucked

string. The string vibrates up-and-down around the equilibrium position. The amplitude of the standing

wave is the maximum displacement in the up direction or down direction of the string from the

equilibrium position. For the transverse wave, the equilibrium position is the imaginary line around

which the wave oscillates. The amplitude is the maximum displacement in the up (crest) or down

(trough) direction of the wave.

The relationship between amplitude and the energy of the wave or vibration

The greater the amplitude, the more work was done to move the medium molecules in the up-and-

down direction, the greater the energy (more kinetic energy and more heat).

The lesser the amplitude, the lesser work was done to move the medium molecules in the up-and-

down direction, the lesser the energy (less kinetic energy and less heat).

Frequency and Wavelength

The relationship between frequency and wavelength is determined by the following series of equations

that have been algebraically rearranged. The product of the frequency of the wave and the wavelength

of the wave is always the wave speed.

amplitude

Wavelength is defined as the distance between two identical positions

on two adjacent or consecutive waves. Wavelength could be crest-to-

crest, trough-to-trough, or node-to-node. In the diagrams, the

wavelength is shown as crest-to-crest.

Wavelength is a distance, and is reported in units of meters. The

diagram to the left shows two different waves. The top wave is a

“high frequency” wave. The bottom wave is a “low frequency” wave.

The top wave has more cycles per unit time whereas the bottom wave

has fewer cycles per unit time.

There is an inverse relationship between frequency and wavelength.

If a wave has a high frequency, the wavelength of the waves is

shorter.

If a wave has a low frequency, the wavelength of the waves is

longer.

fc

cf

f

c

Wave Speed

Wave speed is the speed of the wave moving through a given medium. Treat wave speed like a normal

speed—the wave moves a given distance per unit time. Wave speeds may be reported in units of m/s,

km/hr, or km/s depending on the context of the wave.

Wave speed is denoted by the letter c. This applies to the speed of sound, speed of light, or speed of

seismic waves.

Wave speed: t

dc

Wave speed is dependent on many factors, such as temperature and the medium through which the wave

is moving.

Examples

A guitar string vibrates at a rate of 42000 oscillations per

minute. The speed of sound in air at 20ºC is 343 m/s.

Calculate the frequency (f) of the guitar string in Hz.

Calculate the period (T) of the vibration. (s)

Calculate the wavelength (λ) of the vibration. (m)

m

s

sm

f

c

sf

T

Hzst

cyclesf

49.0700

343

00143.0700

11

700700s 60

000,42

A horn emits a sound with a frequency of 6500 Hz. The speed of

sound in air at 20ºC is 343 m/s.

Calculate the period (T) of the sound waves emitted from

the horn. (s)

Calculate the wavelength (λ) of the sound waves. (m)

m

s

sm

f

c

sf

T

528.0.06500

343

000154.0/s6500

11

A pendulum completes 10 back-and-forth swings in 35

seconds.

Calculate the frequency of the pendulum in Hz.

Calculate the period of the pendulum’s motion.

s

fT

Hzst

cyclesf

5.3286.0

11

286.0286.035

10

f = frequency (Hz)

c = wave speed (m/s)

λ = wavelength (m)

c = wave speed (m/s)

Δd = distance traveled (m)

t = time (s)

A spring oscillates with a frequency of 2.5 Hz.

Calculate the period of the spring’s oscillation.

Calculate how many back-and-forth cycles the pendulum

will make in 1 minute.

150 605.2

40.0/5.2

11

ss

tfCycles

ssf

T

A whale’s song has a frequency of 400 Hz. The speed of sound

passing through seawater at 10ºC is 1530 m/s.

Calculate the period of the sound waves of the whale’s

song.

Calculate the wavelength of the sound waves of the

whale’s song.

m

s

sm

f

c

ssf

T

83.3400

1530

0025.0/400

11

Part 2: Properties of Electromagnetic Radiation (Light)

What Is Light Made Of?

Electromagnetic radiation (EMR) is the technical term for light. Light is radiant energy. Light, or

EMR travels through space and through transparent media as an electromagnetic wave. Electromagnetic

waves have three components: the photon, the traveling electric field, and the traveling magnetic field.

Unlike mechanical waves, EMR can travel through a vacuum like space. It will also travel through any

medium that has a high degree of transmission.

A photon is a compact packet of energy. The photon behaves like a particle because energy is so

concentrated into a very tiny space, but the photon has no mass. Photons give light its energy. When

matter generates light, the matter releases the photon. As the photon moves through space or air, the

photon’s motion and interaction with molecules that it passes creates the electric field and the magnetic

field. The electric field and magnetic field are invisible perpendicular forces. They are always present

and accompany the moving photon.

Classes of Electromagnetic Radiation

There are seven classes of electromagnetic radiation (EMR). Electromagnetic radiation means light,

thus there are seven classes of light.

Gamma rays have the most energy, the

shortest wavelength, and the greatest

frequency. Radiowaves have the lowest

energy, the longest wavelength, and the

lowest frequency. Visible light is the only

class of light that can be detected by the

human eye. The other classes of EMR are

invisible to the human eye.

Gamma rays, x-rays, and ultraviolet radiation

are called ionizing radiation because they

have enough energy to break chemical bonds

in molecules. That makes them dangerous

because gamma, xray, and ultraviolet light can

damage soft body tissues and DNA.

Infrared, microwave, and radiowaves tend not to be not harmful because they have very low energy.

Visible Spectrum

The visible spectrum, sometimes called the color spectrum, is composed of the wavelengths of visible

light. Human eyes can only detect visible light. Human eyes cannot detect the other forms of EMR—

they appear invisible to human eyes.

White light is the total collect of all

wavelengths of color light in the visible

spectrum. If rays of white light are passed

through a glass prism, the double refraction

of the light will separate the white light into

the different wavelengths of color:

ROYGBIV

Violet is the most energetic of the visible

light, with the shortest wavelength, and the

greatest frequency. Conversely, red is the

least energetic of the visible light, with the

longest wavelength, and the lowest

frequency.

The Color of Objects

White light is the total collection of all visible light wavelengths in the visible spectrum. All colors are

present in white light: ROYGBIV. The color of objects, or hue, is determined by which wavelengths of

the color spectrum are absorbed by matter and which wavelengths are reflected by matter. Absorbance

is where matter captures and assimilates energy—energy is absorbed and converted to heat. Reflection

is where waves (light, sound, mechanical waves) bounce off of a surface without changing frequency.

If you see a blue color of an object, like a blue shirt or a blue car that means that the object is

reflecting the blue wavelengths of the visible spectrum (B) and absorbing the other colors (ROYG,

IV).

If you see a red color of an object, like a red flower or a red fire truck, that means that the object is

reflecting the red wavelengths of the visible spectrum (R) and absorbing the other colors (OYGBIV).

The color black is observed when there is an absence of color or visible light. Black may be the result

of 100% absorbance of all visible light by matter, all light is absorbed and none is reflected to the eye.

The dark blackness of space beyond starlight is observed because there is no visible light in interstellar

space. There is, however, light in the blackness of interstellar space in the form of microwave radiation

(microwaves) which cannot be seen with the unaided eye.

Emission of Light

Objects that generate and emit their own

light are described as luminous or having

luminosity. The release of EMR by matter is

called emission. Light is emitted by atoms

when very energetic or excited electrons

(the negatively-charged subatomic particles

that flow around the nuclei of atoms)

“relax” or return to their normal state as

they were before they were excited. One

photon is given off each time an electron

relaxes, forming an EMR wave that is

emitted by the atom. All matter releases at least one form light. The emission of light is dependent on

how the electrons got excited and by the temperature and the type of matter that is emitting the light.

The electrons are excited by energy (heat, other light, kinetic energy, electricity). When the excited

electrons return to their normal state, they release energy as a photon—a wave of light is given off.

Another way that that light can be emitted is through radioactive decay. When certain unstable nuclei of

atoms disintegrate (change the number of protons or neutrons in the nucleus), x-rays or gamma rays are

emitted.

What emits light (all types)?

Very cold interstellar space, temperatures 2-3 Kelvin, contains microwave background radiation.

Objects with temperatures between 3-2500 Kelvin radiate the majority of their heat in the form of

infrared.

Hotter objects 2500-20,000 K radiate visible light and some and ultraviolet light.

Radioactive materials radiate x-rays and gamma rays as their nuclei disintegrate.

Part 3: Interactions of Waves and Light with Matter

Speed of Light

The speed of light (or light speed) in a vacuum such as space is 300,000,000 m/s (three hundred million

meters per second). In one second time, light will travel 300,000,000 meters. The speed of light is the

greatest physical quantity in the universe and represents the uppermost limit of motion. No object or

other energy can travel faster than the speed of light. In contrast, the speed of sound in air at 20ºC is

343 m/s. The speed of light is 874,635 times greater than the speed of sound. Additionally, the speed of

light applies to ALL CLASSES OF EMR. Every type of EMR travels at the speed of light regardless of

their differences in frequency and wavelength: gamma rays travel at 300,000,000 m/s and radio waves

travel at 300,000,000 m/s.

A light year is the distance that light travels in one calendar year. In 1 second, light travels 300,000,000

m. In 1 calendar year, light travels 9.47x1015

m. (9,470,000,000,000,000 m). Light years are used to

quantify very, very large distances between stars and between galaxies. For example, the closest star to

our Sun is called Proxima Centauri (“Near Centaur”). Proxima Centauri lies 4.4 light years away.

Starlight emitted by Proxima Centauri will take 4.4 years to reach our solar system.

As light passes through different materials, the speed of light will be

different. As a general rule, the speed of light decreases as the density of

the material through which it passes increases—the greater the density, the

lower the speed of light through that material. The speed of light through a

vacuum (empty space) is 1.5 times greater than the speed of light through

glass.

Speed of Light

Vacuum: 300,000,000 m/s

Air: 299,000,000 m/s

Water: 256,000,000 m/s

Glass: 200,000,000 m/s

Transmission of Light

If a medium has a high degree of transmission, light will pass through that medium with little

interference, scattering, or diffusion. Air, glass, and still water are transparent media. A transparent

medium will allow light to pass through it. Images can be clearly seen through transparent media.

Translucent media will allow light to pass through the surface into the medium’s interior, however, the

medium will distort or blur the light. Clear images cannot be seen on the other side of translucent media.

Examples of objects that are translucent include milk and gemstones. An opaque medium will not allow

light to pass through it. Light is either absorbed or reflected away from the surface, no light will

penetrate into the medium’s interior. If light shines on an opaque object, a shadow will be projected on

surfaces opposite the light source.

Absorbance of Light

Absorbance is the assimilation of EMR by matter. Absorbance occurs when the photons in EMR waves

(the compact packets of energy) are taken in by the molecules in matter upon which they impact. That

light energy adds kinetic energy to the molecules, which causes the temperature of the matter absorbing

the light to increase (get hotter). If you stand outside on a hot summer day in direct sunlight, sunlight

striking your skin will cause your skin to feel warmer—EMR energy is converted to KE in the

molecules in your skin which causes the increase in temperature. Dark colored objects have the greatest

absorbance. Asphalt, soil, and dark-colored clothing will absorb the majority of visible light rays that

strike their surfaces and reflect very little light. That is why asphalt and soil gets hot very fast in direct

sunlight. In contrast, light colored objects with smoother surfaces will reflect more light and absorb

very little light. Clouds, ice, snow, and light-colored clothing reflect the majority visible light that

strikes their surfaces.

Reflection of Light

Reflection is the redirection of waves (light, sound, or mechanical) by a surface or boundary. The

frequency and wavelength of the waves do not change when they are reflected, only the direction

changes. There are two types of reflection: Perfect reflection and diffuse reflection. Perfect reflection

(left diagram) is where incoming light strikes a smooth reflective surface and the rays of light are

reflected away in parallel. Mirrors and polished metals will create perfect reflection. Diffuse reflection

(right diagram) occurs when incoming light strikes an irregular surface and the rays of light are reflected

away in multiple directions. All non-polished, irregularly shaped objects will produce diffuse reflection.

When perfect reflection occurs, the rays of light

obey the Law of Reflectance. The Law of

Reflectance states: the angle of incidence equals

the angle of reflection. In other words, the angle

of the incoming light before it strikes the reflective

surface must equal the angle of the light leaving or

reflected from the reflective surface. The incident

and reflected angles are measured relative to the

normal ray.

Refraction

Refraction is the bending or change of direction of waves (light, sound, or other mechanical waves) as

the wave passes through a boundary between two media with different densities. Refraction is always

accompanied by the change in direction of the wave and the change in speed. Consider the two

scenarios with light passing between air and water.

Left image: Light from air passes through the boundary into water. The light slows because water is

denser than air and is refracted toward the normal.

Right image: Light from water passes through the boundary into air. The light speeds up because air is

less dense than water and is refracted away from the normal.

Lenses

Double Convex Lens (converging)

A lens is curved, polished glass that uses

refraction to transmit or focus the light

rays passing through it. Converging

lenses focus (bring together) light rays to

a common point where all of the light

rays cross. Diverging lenses cause light

rays to spread out or diverge.

A double convex lens is an example of a

converging lens. Converging lenses bring

light together, intensifying the incoming

light rays. Their images appear larger

and clearer. Notice that as the parallel

rays of light pass through the lens, the

rays are refracted toward each other and

eventually cross at the same point beyond

the lens, called the focal point. The

lenses in magnifying glasses,

microscopes, and refracting telescopes

are converging lenses.

projected onto surfaces. The lenses in

projectors are diverging lenses.

A double concave lens is an example of a diverging lens. Notice that as the parallel rays of light pass

through the lens, the rays diverge or spread out away from each other. Diverging lenses increase the

size of real images that are Converging and diverging lenses have focal points and focal lengths. The

focal point or focus is the locus where light rays converge or cross each other. The focal length is the

Double Concave Lens (diverging)

distance between the geometric center of the lens and the focal point. For the double convex lens, light

converges at the focal point on the side of the lens opposite the light source. Real images viewed at the

focal point are enlarged and clear. Images viewed at a distance less than the focal length are blurry but

right-side up. Images viewed at a distance greater than the focal length are blurry and upside-down. For

the double concave lens, the focal point is imaginary and located on the same side as the light source.

Diffraction

Diffraction is the bending of waves (light, sound, mechanical waves) around obstacles and the spreading

out of waves (light, sound, mechanical) that pass through small openings. Diffraction

Left diagram: It shows waves being intercepted by a boundary (wall) with a small opening. Most of the

wave is absorbed by the boundary, a small fraction of the wave passes through the opening. Once the

portion of the wave passes through the opening, the wave begins to spread out. The farther way travels

beyond the opening, the greater the wave will spread out.

Right diagram: It shows waves being intercepted by an obstacle. The obstacle absorbs the portion of

wave that contacts the obstacle. The remainder of the wave passes unobstructed on either side of the

obstacle. Once past the obstacle, the waves on either side of the obstacle spread out. Immediately

behind the obstacle is a wave shadow.

Luminosity and Brightness

Objects that generate their own light are characterized as being luminous. Most luminous objects

produce light by incandescence. Incandescence is the emission of visible light by matter when matter is

heated to very hot temperatures. Incandescent light bulbs emit white light when the tungsten filament is

heated to > 2000ºC. The very hot gases in fire glow by incandescence. Visible starlight is the result of

incandescence because the surfaces of stars are very hot.

Luminosity is the power of light energy released by a light emitting source. Luminosity, or light power,

is measured in the units of Watts. For example, the power rating of light bulbs is reported in Watts

(Joule/s). A 100 Watt light bulb releases 100 Joules of radiant energy per second. In other words, in 1

second, a 100 Watt light bulb releases 100 Joules of energy. The greater the luminosity, the more light

waves and more photons are released by the light emitting source. The lower the luminosity, the lesser

the light waves and fewer photons are released by the light emitting source. Brightness, or the intensity

of light as seen by an observer, is controlled by three factors: (1) the luminosity of the light source, and

(2) the distance between the light source and the observer, and (3) the amount of light scattering or

interference between the source and the observer.

Scattering is the random redirection or reflection of light rays as light passes through air. The oxygen

and nitrogen gas molecules in the atmosphere scatter some of the violet, indigo, and blue wavelengths of

the visible spectrum. This is why the daytime sky is bluish white in color. Very tiny suspended dust

and ash particles, pollution aerosols (smog), and cloud droplets scatter light as well. On clear days,

visibility is much greater. On days with haze, smog, or cloudy conditions, visibility is limited because

most of the light passing through those clouds or smog zones is scattered and little light is diffused to the

eye.

Luminosity

The greater the luminosity of the source, the more light rays and photons released by the

source, the brighter the light will appear.

The lesser the luminosity of the source, the fewer light rays and photons released by the

sources, the dimmer the light will appear.

Distance

The closer the observer is to the light source, a greater percentage of light rays are

directed to the eye, the brighter the light will appear.

The farther away the observer is to the light source, the lower percentage of light rays are

directed to the eye, the dimmer the light will appear.

Scattering

The lesser the scattering, the fewer light rays are randomly reflected by suspended dust,

particles, and gas molecules in the atmosphere, the brighter the light will appear.

The greater the scattering, the more light rays are randomly reflected by suspended dust,

particles, and gas molecules in the atmosphere, the dimmer the light will appear.

Part 4: Sound and Sound Waves

Sound Waves

Sound is energy that moves as a traveling

vibration in the form of longitudinal

waves. Like all mechanical waves, sound

waves propagate or travel through

matter—solids, fluids, and gases—but

cannot travel through a vacuum like space.

The compressions of the sound wave are

called wave fronts. Wave fronts are

traveling pulses of higher pressure created

when air molecules are bunched up. Wave

fronts carry the energy of the sound wave.

When the wave fronts impact the ear or sound detector, they carry the intensity of the sound, the sound

is loud. The greater the number of molecules bunched up at the wave front, the thicker the wave front,

the greater the pressure, the louder the sound will be perceived. Conversely, the rarefactions or the

regions between wave fronts where air molecules are spread out or expanded, carries little intensity of

the sound, the sound is very soft or no sound. The sinusoidal wave below the longitudinal wave in the

diagram above is to provide reference. The crests represent the wave fronts or regions of higher

pressure—loud sound. The troughs represent rarefactions or regions of lower pressure—soft sound.

Speed of Sound

The speed of sound is much lower than the speed of light. This can be observed during a thunderstorm.

One always sees a lighting strike before hearing the thunder. Light travels through air at 299,000,000

m/s. In contrast, at 20ºC, sound travels through air at 343 m/s. Light travels ~872,000 times faster than

sound. The two greatest factors affecting the speed of sound is density and temperature of the medium

through which sound travels.

Sound travels faster through denser materials.

Sound travels slower through lesser dense

materials. This is true because sound travels as a

longitudinal wave, a moving vibration. If

molecules are closer together and packed in a tight

configuration, the vibration and wave fronts can

easily move from molecule to the next molecule,

bunching them up easily. Sound travels fastest

through dense solids. Sound travels slowest

through gases.

Speed of Sound

Air 20ºC: 343 m/s

Ethanol 25ºC: 1270 m/s

Water 25ºC: 1500 m/s

Lead: 2160 m/s

Glass: 5100 m/s

Steel: 5900 m/s

Speed of Sound in Air

Air 0ºC: 331 m/s

Air 10ºC: 337 m/s

Air 20ºC: 343 m/s

Air 30ºC: 349 m/s

Air 40ºC: 355 m/s

Sound travels faster through hotter materials. Sound travels slower through cooler materials. This is

true because sound waves are traveling vibrations in a longitudinal wave. They are kinetic energy. If

the material is hotter, the kinetic energy in the matter is greater. Thus, as the wave passes through the

material with the greater kinetic energy, the vibrations are passed through faster. If the wave passes

through cooler materials with lesser kinetic energy, the vibrations are passed through slower.

The speed of sound, c, is equal to the distance that sound travels divided by the time of travel:

t

dc

.

Objects that move at subsonic speeds are moving slower than the speed of sound. Objects that move at

transonic speeds are moving at the speed of sound. Objects that move at supersonic speeds are moving

at speeds greater than the speed of sound. When objects “break the sound barrier”, the wave fronts or

compressions of the sound generated by the supersonic object collect and become thicker and more

intense, called a shockwave. When the shockwave passes by, a thunderous violent roar is created called

the sonic boom.

Frequency and Wavelength of Sound

Frequency is the number of vibrations, waves, or cycles passing a given position per second.

Wavelength is the distance between two identical positions on two consecutive waves. Remember,

frequency is inversely proportional to wavelength.: The higher the frequency, the shorter the

wavelength; the lower the frequency, the longer the wavelength. The frequency of sound affects pitch.

Pitch is the quality of sound received by and interpreted by the human ear. If sound has lower

frequency, the ear detects sound that is bass (low). If sound has a higher frequency, the sound is more

shrill (high). A tuba produces low frequency sound (200-300 Hz) which has a more bass pitch. A

trumpet produces a medium frequency sound (600-900 Hz). A flute produces a high frequency sound

that has a more shrill pitch (1000-3000 Hz). The sounds emitted by pianos encompass a very large

range of frequency (30-4000 Hz).

The audible range of typical human hearing is 20 Hz to 20,000 Hz. Most human ears can detect sound

with frequencies in that range. Humans cannot hear or detect sound outside of that range. Most

mammals can hear higher frequency sound. Infrasonic waves are sound waves that have frequencies

below 20 Hz. Ultrasonic waves are sounds that have frequencies greater than 20,000 Hz. Some seismic

waves, whale songs, and thunder are infrasonic. Bats and dolphins emit ultrasonic pulses for

echolocation.

The relationship between frequency and wavelength of sound is determined by the following series of

equations that have been algebraically rearranged. The product of the frequency of the wave and the

wavelength of the wave is always the speed of sound (wave speed).

fc

cf

f

c

c = wave speed (m/s)

Δd = distance traveled (m)

t = time (s)

f = frequency (Hz)

c = wave speed (m/s)

λ = wavelength (m)

Reflection and Refraction of Sound

An echo is the reflection of sound waves

off of a solid surface or boundary.

Sound is emitted by the sound producing

source, soundwaves strike the surface or

boundary, and are reflected back to the

source. For a true echo, the

sender/receiver must hear distinctly the

sound when it was originally emitted

and the reflected sound. The emitted

sound and reflected sound should not

overlap.

A reverberation is when the reflected sound waves overlap with emitted sound waves. There is not

enough time between when the original sound wave emitted by the source and the reflected sound

returns. The original sound and reflected sound cannot be distinctly heard.

Sound waves (like all waves) will refract.

Refraction is the bending of waves as waves pass through a boundary from one medium into another.

Remember, wave speed also changes. In the diagram to the upper left, sound waves are being refracted as

sound passes through air of different temperatures. When the wave fronts encounter warmer air, sound waves

speed up and bend away from the ground. When the wave fronts encounter cooler air, sound waves slow and

bend toward the ground. In the diagram to the upper right, sound waves cross the boundary from air into

water. Notice that the sound waves speed up and change direction as they pass into the water because water is

denser than air.

Resonance

Resonance is the ability of objects to vibrate or oscillate when waves of selective frequencies pass

through them. For the object to vibrate or sway or oscillate, the object must have a fundamental

frequency (the frequency that it will cause it to vibrate) that matches or is an integer value of the

frequency of the wave passing through it.

Resonance occurs when there is a forced

transfer of waves or vibrations from a source (an

object that is emitting vibrations or sound) and

another object. For example, if you strike a

tuning fork, the prongs begin to vibrate and emit

sound waves. The air transfers the sound

waves to the adjacent tuning fork. The

frequency of the impacting wave fronts causes

the second tuning fork to vibrate. The second

tuning fork had a fundamental frequency that

was the same, or an integer value of the first

tuning fork, otherwise the second turning fork

would not have vibrated.

Another example of resonance is during earthquakes. Seismic waves passing through the crust will be

transferred upward from the crust into the foundations of buildings. Very tall buildings, like skyscrapers,

may sway during earthquakes, not because of the shaking at the ground, but because of the resonance of

the seismic waves transferring wave energy upward to the structure. If the structure has the same

fundamental frequency as the seismic wave, the structure will sway with a frequency equal to the

frequency of the seismic wave.

Volume and Sound Intensity

Volume is the loudness of sound. Intensity is the power of sound energy at a given distance away from

the sound emitting sources. The two are related. Volume is a function of the amplitude of the sound

wave. The greater the air is compressed at the wave front, the more molecules bunched up in the

condensation, the louder the volume will be. The intensity of sound is greatest at the sound emitting

source. As sound waves move away from the source, the sound waves spread out into thinner and

thinner wave fronts. Because of the thinning out of the waves as they move away from the source, the

volume and intensity of the sound decreases. A person standing 1 meter in front of a music speaker will

hear more intense sound and louder volume than a person standing 10 meters away, who will hear more

intense sound and louder volume than a person standing 50 meters away.

Sound intensity is measured in decibels (ten-bels). Decibels is a base-10 logarithmic scale of measure

that characterizes the intensity of sound.

Decibel Loudness Object

0 Threshold of hearing

10 Very faint Watch ticking

20 Very faint Whisper

30 Faint Quiet conversation

40 Faint Tapping foot

50 Moderate Normal Conversation

60 Moderate Normal car engine

70 Loud Rock music on radio

80 Loud Alarm clock

90 Very loud Machines in factory

100 Very loud Lawn mower

110 Deafening Train locomotive

120 Deafening Plane taking off