Waves

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1. A wave is a disturbance of a medium which transports energy through a medium without permanently transporting matter. In a wave, particles of the medium are temporily displaced and then return to their original position.

Amplitude (A) - maximum displacement of particle from its equilibrium.

Frequency - number of waves that pass a point in a unit of time.
Wavelength (A to F)(B to G)(D to I)(E to J) - distance between two point in phase. It is symbolised by l (lambda).

Displacement: how far a particle is from equalibrium, it is a distance with a direction since it is a vector quantity; symbol is d and SI unit is m (for meters).
Speed - distance travelled by wave in unit time: the speed with which the wave moves through a medium is the product of the wavelength and the frequency; SI unit is m/s (v = ln or v = l f)

A Transverse Wave: As a Transverse wave passes through a point, the particles vibrate at right angles to the direction in which the wave is moving, eg electromagnetic waves

A Longitudinal Wave: As a Longitudinal wave passes through a point, the particles vibrate parallel to the direction in which the wave is moving, eg sound

4. An Electromagnetic wave consist of repeating patterns of electric and magnetic forces. They exist is the form of a transverse wave. eg light waves, radio waves, microwaves, X-rays, etc. Electromagnetic waves require a vibrating energy source but do not require a medium. All Electromagnetic waves have a velocity of approximately 3 x 10^8 m/s however their frequency (f), wavelength l (lamba) and energy levels (amplitude) vary.

A Mechanical wave is a disturbance that must pass through a medium. eg sound waves, water waves, etc. These require a vibrating energy source to create the disturbance and an elastic medium to transfer the disturbance. The medium does not absorb any energy.

5. Displacement Time Graphs :
Displacement Time Graphs are drawn to represent the motion of a single particle in an elastic medium as the result of transverse or longitudinal waves passing through
- a compression is a crest and rerefraction a trough
- Displacement refers to how far a particle is from equalibrium.
- Time refers to the period(T) to complete 1 wave.
To produce a Displacement Time Graph all you need is the period. For accurate drawing you will also need an amplitude.

Displacement Distance Graph
-Distance refers to the distance between two particles is phase (wavelength)
-Displacement refers to how far a particle is from equalibrium.
To produce a Displacement Distance Graph all you need is the wavelength. For accurate drawing you will also need an amplitude.

6. The wave equation is expresses as V= ln where
V = Velocity (m/s)
l = Frequency (Hz)
n = Wavelength (m)
Period(t) = 1/Frequency

7. A ray approaching and reflecting off of a flat surface, follows the law of reflection.

The incident ray (I) is the ray approaching the mirror.
The reflected ray (R) is the ray which leaves the mirror.
The Normal is a line that can be drawn perpendicular to the surface where the incident ray strikes the mirror. The normal line divides the angle between the incident ray and the reflected ray into two equal angles.
The angle between the incident ray and the normal is known as the angle of incidence.
The angle between the reflected ray and the normal is known as the angle of reflection.

Fixed End Reflections
-the reflected pulse is inverted. If a crest is incident towards a fixed end boundary, it will reflect and return as a trough. If a trough is incident towards a fixed end boundary, it will reflect and return as a crest.
-the speed of the reflected pulse is the same as the speed of the incident pulse
-the wavelength of the reflected pulse is the same as the wavelength of the incident pulse
-the amplitude of the reflected pulse is less than the amplitude of the incident pulse

Free End Reflections
When the incident pulse reaches the the end of the medium, the last particle of the rope can no longer interact with the first particle of the pole. Since the rope and pole are no longer attached and interconnected, they will slide past each other. So when a crest reaches the end of the rope, the last particle of the rope receives the same upward displacement; only now there is no adjoining particle to pull downward upon the last particle of the rope to cause it to be inverted. The result is that the reflected pulse is not inverted. When a crest is incident upon a free end, it returns as a crest after reflection; and when a trough is incident upon a free end, it returns as a trough after reflection. -Inversion is not observed in free end reflection.
-the speed of the reflected pulse is the same as the speed of the incident pulse
-the wavelength of the reflected pulse is the same as the wavelength of the incident pulse
-the amplitude of the reflected pulse is less than the amplitude of the incident pulse

8. Refraction of waves involves a change in the direction of waves as they pass from one medium to another. Refraction, or bending of the path of the waves, is accompanied by a change in speed and wavelength of the waves.
So if the medium (and its properties) are changed, the speed of the waves are changed. Thus waves passing from one medium to another will undergo refraction.
Refraction of sound waves is most evident in situations in which the sound wave passes through a medium with gradually varying properties.
For light, optical density affects it. For sound, it is dependant on the properties of the material.
Rays are refracted only when it hits a boundary at an angle. It is not refracted if it strikes perpendicular to the boundary.

When passing from air into glass, both the speed and the wavelength decrease. Finally, and most importantly, the light is observed to change directions as it crosses the boundary separating the air and the glass. The transmitted wave experiences this refraction at the boundary. As seen in the diagram below, each individual wavefront is bent only along the boundary. Once the wavefront has passes across the boundary, it travels in a straight line. A ray is drawn perpendicular to the wavefronts; this ray represents the direction which the light wave is traveling. Observe that the ray is a straight line inside of each of the two media, but bends at the boundary.
It is due to the difference of speed of one side of the wave compared to the other.

When light enters a more optically dense medium, its speed is reduced. The angle of refraction is less than the angle of incidence. The refracted ray is said to be bent "toward the normal."

When light enters a less optically dense medium, its speed is increased. The angle of refraction is greater than the angle of incidence. The refracted ray is said to be bent "away from the normal."

Sound waves are known to refract when traveling over water. Even though the sound wave is not exactly changing media, it is traveling through a medium with varying properties; thus, the wave will encounter refraction and change its direction. Since water has a moderating effect upon the temperature of air, the air directly above the water tends to be cooler than the air far above the water. Sound waves travel slower in cooler air than they do in warmer air. For this reason, the portion of the wavefront directly above the water is slowed down, while the portion of the wavefronts far above the water speeds ahead. Subsequently, the direction of the wave changes, refracting downwards towards the water. This is depicted in the diagram at the right.

9. Diffraction involves a change in direction of waves as they pass through an opening or around a barrier in their way. We can see that water waves have the ability to travel around corners, around obstacles and through openings. The amount of diffraction (the sharpness of the bending) increases with increasing wavelength and decreases with decreasing wavelength. In fact, when the wavelength of the waves are smaller than the obstacle or opening, no noticeable diffraction occurs.

Diffraction of sound waves is commonly observed; we notice sound diffracting around corners or through door openings, allowing us to hear others who are speaking to us from adjacent rooms. Many forest-dwelling birds take advantage of the diffractive ability of long-wavelength sound waves. Owls for instance are able to communicate across long distances due to the fact that their long-wavelength hoots are able to diffract around forest trees and carry farther than the short-wavelength tweets of song birds. Low-pitched (high wavelength) sounds always carry further than high pitched (low wavelength) sounds.

Bats use high frequency (low wavelength) ultrasonic waves in order to enhance their ability to hunt. The typical prey of a bat is the moth - an object not much larger than a couple of centimeters. Bats use ultrasonic echolocation methods to detect the presence of bats in the air. They use ultrasoundbecause of the physics of diffraction. As the wavelength of a wave becomes smaller than the obstacle which it encounters, the wave is no longer able to diffract around the obstacle, instead the wave reflects off the obstacle. Bats use ultrasonic waves with wavelengths smaller than the dimensions of their prey. These sound waves will encounter the prey, and instead of diffracting around the prey, will reflect off the prey and allow the bat to hunt by means of echolocation. The wavelength of a 50 000 Hz sound wave in air (speed of approximately 340 m/s) can be calculated as follows
wavelength = speed/frequency
wavelength = (340 m/s)/(50 000 Hz)
wavelength = 0.0068 m

The wavelength of the 50 000 Hz sound wave (typical for a bat) is approximately 0.7 centimeters, smaller than the dimensions of a typical moth.

Foghorns have very low pitches because sounds with low pitches have a long wavelength. This is important because a long wavelength means that the sound wave can pass around barriers, like rocks, easily. The longer the wave's length the easier it is for the wave to do this.

10. The principle of superposition is sometimes stated as follows: "When two waves interfere, the resulting displacement of the medium at any location is the algebraic sum of the displacements of the individual waves at that same location." Wave interference is the phenomenon which occurs when two waves meet while traveling along the same medium.

11. Consider two pulses of the same amplitude traveling in different directions along the same medium. Each crest has an amplitude of +1 unit (the positive indicates an upward displacement as would be expected for a crest) and has the shape of a sine wave. As the sine crests move towards each other, there will eventually be a moment in time when they are completely overlapped. At that moment, the resulting shape of the medium would be a sine crest with an amplitude of +2 units. The diagrams below depict the before- and during interference snapshots of the medium for two such crests. The individual sine crests are drawn in red and blue and the resulting displacement of the medium is drawn in green.

This type of interference is sometimes called constructive interference. Constructive interference is a type of interference which occurs at any location along the medium where the two interfering waves have a displacement in the same direction. In this case, both waves have an upward displacement; consequently, the medium has an upward displacement which is greater than the displacement of the two interfering pulses. Constructive interference is observed when a crest meets a crest; but it is also observed when a trough meets a trough as shown in the diagram below.

In this case, a sine trough with an amplitude of -1 unit (negative means a downward displacement) interferes with a sine trough with a displacement of -1 unit. These two troughs are drawn in red and blue. The resulting shape of the medium is a sine trough with a maximum displacement of -2 units.

Destructive interference is a type of interference which occurs at any location along the medium where the two interfering waves have a displacement in the opposite direction. For instance, when a sine crest with an amplitude of +1 unit meets a sine trough with an amplitude of -1 unit, destructive interference occurs. This is depicted in the diagram below.

In the situation in the diagram above, the interfering pulses have the same maximum displacement but in opposite directions. The result is that the two pulses completely destroy each other when they are completely overlapped. At the instant of complete overlap, there is no resulting disturbance in the medium. This "destruction" is not a permanent condition. In fact, to say that the two waves destroy each other can be partially misleading. When it is said that the two pulses "destroy each other," what is meant is that when overlapped, the effect of one of the pulses on the displacement of a given particle of the medium is "destroyed" or canceled by the effect of the other pulse. When two pulses with opposite displacements (i.e., a crest and trough) meet at a given location, the upward pull of the crest is balanced (canceled or "destroyed") by the downward pull of the trough. Once the two pulses pass through each other, there is still a crest and a trough heading in the same direction which they were heading before interference. Destructive interference leads to only a momentary condition in which the medium's displacement is less than the displacement of the largest-amplitude wave.

The two interfering waves do not need to have equal amplitudes in opposite directions for destructive interference to occur. For example, a crest with an amplitude of +1 unit could meet a trough with an amplitude of -2 units; the resulting displacement of the medium during complete overlap is -1 unit.

This is still destructive interference since the two interfering waves have opposite displacement. In this case, the destructive nature of the interference does not lead to complete cancellation.

12. Beats are the periodic and repeating fluctuations heard in the intensity of a sound when two sound waves of very similar frequencies interfere with one another. The diagram below illustrates the wave interference pattern resulting from two waves (drawn in red and blue) with very similar frequencies. A beat pattern is characterized by a wave whose amplitude is changing at a regular rate. Observe that the beat pattern (drawn in green) repeatedly oscillates from zero amplitude to a large amplitude, back to zero amplitude throughout the pattern. Points of constructive interference (C.I.) and destructive interference (D.I.) are labeled on the diagram. When constructive interference occurs, a loud sound is heard; this corresponds to a peak on the beat pattern (drawn in green). When destructive interference occurs, no sound is heard; this corresponds to a point of no displacement on the beat pattern. Since there is a clear realtionship between the amplitude and the loudness, this beat pattern would be consistent with a wave which varies in volume at a regular rate.

Tuning:
A piano tuner frequently utilizes the phenomenon of beats to tune a piano string. She will pluck the string and tap a tuning fork at the same time. If the two sound sources - the piano string and the tunng fork - produce detectable beats then their frequencies are not identical. She will then adjust the tension of the piano string and repeat the process until the beats can no longer be heard. As the piano string becomes more in tune with the tuning fork, the beat frequency will be reduced and approach 0 Hz. When beats are no longer heard, the piano string is tuned to the tuning fork; that is, they play the same frequency.

Guitar:
The tuning fork presents the reference frequency that the first string will be tuned to. The tension of the first string is adjusted until it matches the frequency of the tuning fork. If the frequencies of the string and fork match they will resonate and be perceived as one amplified sound. (Resonance refers to the matching of frequencies) If the frequencies do not match they will produce (as for the superpositioning principle) a sound of repetitive amplitude modulation (wavering/throbbing) known as beats. The act of tuning is to eliminate beats. The string tension is therefore adjusted until no beats are detected. Once the first string is 'set', the other strings can be tuned by simlarly adjusting their tension so that the set string resonates with one of its harmonic producing positions. These harmonic positions are found in precise positions along the fret board of the guitar. Each string can thus be tuned to the one before by eliminating beats between harmonic positions.

13. The beat frequency refers to the rate at which the volume is heard to be oscillating from high to low volume. For example, if two complete cycles of high and low volumes are heard every second, the beat frequency is 2 Hz. The beat frequency is always equal to the difference in frequency of the two notes which interfere to produce the beats. So if two sound waves with frequencies of 256 Hz and 254 Hz are played simultaneously, a beat frequency of 2 Hz will be detected. Beats were produced in a classroom demonstration using two tuning forks. The tuning forks had near identical frequencies. The result was that the two tuning forks produced sounds with slightly different frequencies which interfered to produce detectable beats. The human ear is capable of detecting beats with frequencies of 7 Hz and below.

A tuning fork with a frequency of 440 Hz is played simultaneously with a fork with a frequency of 437 Hz. How many beats will be heard over a period of 10 seconds?
Answer: 30 beats
The beat frequency will be 3 Hz; thus in 10 seconds, there should be 30 beats

14. Standing waves are produced by the superpositioning of two identical waves, 180^o out of phase, travelling in opposite directions through a medium. Identical meaning they have the same frequency, amplitude, speed and wavelength. Standing Waves generally occurs when a wave superposes with its reflection from a rigid barrier.

16. One characteristic of every standing wave pattern is that there are points along the medium which appear to be standing still. These points, sometimes described as points of no displacement, are referred to as nodes. There are other points along the medium which undergo vibrations between a large positive and and large negative displacement. These are the points which undergo the maximum displacement during each vibrational cycle of the standing wave. In a sense, these points are the opposite of nodes, and so they are called antinodes. A standing wave pattern always consist of an alternating pattern of nodes and antinodes. The animation shown below depicts a rope vibrating with a standing wave pattern; the nodes and antinodes are labeled on the diagram. When a standing wave pattern is established in a medium, the nodes and the antinodes are always located at the same position along the medium; they are "standing still." It is this characteristic which has earned the name "standing wave."

The nodes and antinodes in a standing wave pattern (like all the points along the medium) are formed as the result of the interference of two waves. The nodes are produced at locations where destructive interference occurs. For instance, nodes form at locations where a crest of one wave meets a trough of a second wave; or a half-crest of one wave meets a half-trough of a second wave; or a quarter-crest of one wave meets a quarter-trough of a second wave; etc. Antinodes, on the other hand, are produced at locations where constructive interference occurs. For instance, if a crest of one wave meets a crest of a second wave, a point of large positive displacement results.
Similarly, if a trough of one wave meets a trough of a second wave, a point of large negative displacement results. Antinodes are always vibrating back and forth between these points of large positive and large negative displacement; this is because during a complete cycle of vibration, a crest will meet a crest; and then one-half cycle later, a trough will meet a trough. Because antinodes are vibrating back and forth between positive and negative displacements, a diagram of a standing wave is sometimes depicted by drawing the shape of the medium at an instant in time and at an instant one-half vibrational cycle later.

Nodes and antinodes should not be confused with crests and troughs. When the motion of a traveling wave is discussed, it is customary to refer to a point of large maximum displacement as a crest and a point of large negative displacement as a trough. These represent points of the disturbance which travel from one location to another through the medium. An antinode on the other hand is a point on the medium which is staying in the same location. Furthermore, an antinode vibrates back and forth between a large upward and a large downward displacement. And finally, nodes and antinodes are not actually part of a wave. Recall that a standing wave is not actually a wave but rather a pattern which results from the interference of two or more waves; since a standing wave is not technically a wave, then an antinode is not technically a point on a wave. The nodes and antinodes are merely points on the medium which make up the wave pattern.

Most instruments involve more than a single vibrating body. For example, in a violin, both the strings and the violin body vibrate.
-vibrating strings (guitar, piano, violin)
-vibrating membranes (drums)
-vibrating air columns (flute, oboe, organ)
-vibrating steel bars (xylophone)

Strings produce transverse waves; sound is produced as string compresses and rarefacts air

The law of strings requency is increased as string length is decreased
-frequency is increased as string diameter is decreased
-frequency is increased as string tension is increased
-frequency is increased as string density is decreased

Pipes produce standing waves
Closed pipes — an antinode is always at an open end and a node is always at a closed end
Open pipes — an antinode is at each open end

Instruments produce standing waves. In any instrument, several harmonics are excited at the same time and the resultant sound is the superposition of these components.

Notice: There are no even-numbered harmonics in a closed pipe. A closed pipe only produces odd harmonics. In strings and open pipes,

This information is summarized in the table below for strings.

Harm. #	# of Waves in String	# of Nodes	# of Anti- nodes	Length- Wavelength Relationship
1	1/2	2	1	l = (2/1)*L
2	1 or 2/2	3	2	l = (2/2)*L
3	3/2	4	3	l = (2/3)*L
4	2 or 4/2	5	4	l = (2/4)*L
5	5/2	6	5	l = (2/5)*L

There are a variety of other low energy vibrational patterns which could be established in the string; for guitar strings, each pattern is characterized by some basic traits:
There is an alternating patterns of nodes and antinodes.
There are either a half-number or a whole-number of waves within the pattern established on the string.
Nodal positions (points of no displacement) are established at the ends of the string where the string is clamped down in a fixed position.
One pattern is related to the next pattern by the addition (or subtraction) of one or more nodes (and anti-nodes).

When the guitar is played, the string, sound box and surrounding air vibrate at a set of frequencies to produce a wave with a mixture of harmonics. The exact composition of that mixture determines the timbre or quality of sound which is heard. If there is only a single harmonic sounding out in the mixture (in which case, it wouldn't be a mixture), then the sound is rather pure-sounding. On the other hand, if there are a variety of frequencies sounding out in the mixture, then the timbre of the sound is rather rich in quality.

17. Free or natural vibration occurs when an object is struck and then allowed to vibrate without further inerference.
Forced vibration occurs when a body vibrates at a frequency that is not is natural frequency.
The amplitude of a forced vibration system varies as the frequency of the driving force alters. The closer the forced vibration is to the natural frequency the louder the sound will be. As less energy is required to vibrate the object, hence it is easier to vibrate and the left over energy is used to emphasize the intensity of the sound.

19. Resonance is the effect that occurs when a body vibrates at its natural frequency or when one object vibrating at the same natural frequency of a second object forces that second object into vibrational motion.
The word resonance comes from Latin and means to "resound" - to sound out together with a loud sound. Resonance is a common cause of sound production in musical instruments.

The wineglass is able to vibrate at a number of natural frequencies. If the singer's voice has a strong frequency component that corresponds to one of these natural frequencies, sounds are coupled into the glass. Setting up forced vibrations that will efficiently build constructively (resonance), and increase the amplitude and the amount of vibration experienced by the particles. Resulting in large stresses in the glass structure that causes it to shatter (if the the sound can be sustained long enough).

In class experiments, one of our models of resonance in a musical instrument included the resonance tube (a hollow cylindrical tube) immersed in a cylinder of water and forced into vibration by a tuning fork. The tuning fork was the object which forced the air inside of the resonance tube into resonance. As the tines of the tuning fork vibrated at their own natural frequency, they created sound waves which impinged upon the opening of the resonance tube. These impinging sound waves produced by the tuning fork forced air inside of the resonance tube to vibrate at the same frequency. Yet, in the absence of resonance, the sound of these vibrations is not loud enough to discern. Resonance only occurs when the first object is vibrating at the natural frequency of the second object. So if the frequency at which the tuning fork vibrates is not identical to one of the natural frequencies of the air column inside the resonance tube, resonance will not occur and the two objects will not sound out together with a loud sound. But the resonance tube can be moved up and down within the water, thus decreasing or increasing the length of the air column. An increase in the length of a vibrational system (here, the air in the tube) increases the wavelength and decreases the natural frequency of that system. Conversely, a decrease in the length decreases the wavelength and increases the natural frequency. So by moving the resonance tube up and down within the water, the natural frequency of the air in the tube could be matched to the frequency at which the tuning fork vibrates. When the match is achieved, the tuning fork forces the air column inside of the resonance tube to vibrate at its own natural frequency and resonance is achieved. And always, the result of resonace is a big vibration ie a loud sound.

The familiar "sound of the sea" which is heard when a seashell is placed up to your ear is also explained by resonance. Even in an apparently quiet room, there are sound waves with a range of frequencies. These sounds are mostly inaudible due to their low intensity. This so-called background noise fills the seashell, causing vibrations within the seashell. But the seashell has a set of natural frequencies at which it will vibrate. If one of the frequencies in the room forces air within the seashell to vibrate at its natural frequency, a resonance situation is created. And always, the result of resonace is a big vibration - that is, a loud sound. In fact, the sound is loud enough to hear. So the next time you hear the "sound of the sea" in a seashell, remember that all that you are hearing is the amplification of one of the many background frequencies in the room.

20. The absolute intensity of sound is a measure of the sound energy carried by waves per second through an area of one metre square. It is measured in watts per square metre ( W m^-2).

The greater the amplitude of vibrations of the particles of the medium, the greater the rate at which energy is transported through it, and the more intense that the sound wave is. Intensity is the energy/time/area; and since the energy/time ratio is equivalent to the quantity power, intensity is simply the power/area.

As a sound wave carries its energy through a two-dimensional or three-dimensional medium, the intensity of the sound wave decreases with increasing distance from the source.

The decrease in intensity with increasing distance is explained by the fact that the wave is spreading out over a circular (2 dimensions) or spherical (3 dimensions) surface and thus the energy of the sound wave is being distributed over a greater surface area. The diagram at the right shows that the sound wave in a 2-dimensional medium is spreading out in space over a circular pattern. Since energy is conserved and the area through which this energy is transported is increasing, the power (being a quantity which is measured on a per area basis) must decrease. The mathematical relationship between intensity and distance is sometimes referred to as an inverse square relationship. As the intensity varies inversely with the square of the distance from the source. So if the distance from the source is doubled (increased by a factor of 2), then the intensity is quartered (decreased by a factor of 4). Similarly, if the distance from the source is quadrupled, then the intensity is decreased by a factor of 16. Applied to the diagram at the right, the intensity at point B is one-fourth the intensity as point A and the intensity at point C is one-sixteenth the intensity at point A. Since the intensity-distance relationship is an inverse relationship, an increase in one quantity corresponds to a decrease in the other quantity. And since the intensity-distance relationship is an inverse square relationship, whatever factor by which the distance is increased, the intensity is decreased by a factor equal to the square of the "distance change factor." The sample data in the table below illustrate the inverse square relationship between power and distance.

Humans are equipped with very sensitive ears capable of detecting sound waves of extremely low intensity. The faintest sound which the typical human ear can detect has an intensity of 1*10^-12 W/m². This intensity corresponds to a pressure wave in which a compression of the particles of the medium increases the air pressure in that compressional region by a mere 0.3 billionths of an atmosphere. A sound with an intensity of 1*10^-12 W/m² corresponds to a sound which will displace particles of air by a mere one-billionth of a centimeter. The human ear can detect such a sound. This faintest sound which the human ear can detect is known as the threshold of hearing. The most intense sound which the ear can safely detect without suffering any physical damage is more than one billion times more intense than the threshold of hearing.

While the intensity of a sound is a very objective quantity which can be measured with sensitive instrumentation, the loudness of a sound is more of a subjective response which will vary with a number of factors. The same sound will not be perceived to have the same loudness to all individuals. Age is one factor which effects the human ear's response to a sound. Quite obviously, your grandparents do not hear like they used to. The same intensity sound would not be perceived to have the same loudness to them as it would to you. Furthermore, two sounds with the same intensity but different frequencies will not be perceived to have the same loudness. Because of the human ear's tendency to amplify sounds having frequencies in the range from 1000 Hz to 5000 Hz, sounds with these intensities seem louder to the human ear. Despite the distinction between intensity and loudness, it is safe to state that the more intense sounds will be perceived to be the loudest sounds.

21. Since the range of intensities which the human ear can detect is so large, the scale which is frequently used by physicists to measure intensity is a scale based on multiples of 10. This type of scale is sometimes referred to as a logarithmic scale.

The units of the intensity level of sound are decibel, or dB, in honor of Alexander Graham Bell. Since the intensity level is based on a log scale, every change of 10 dB means that the sound is 10 times louder; a change of 20 dB means that the sound is 10², or 100 times louder. A sound which is 10*10*10 or 1000 times more intense ( 1*10^-9 W/m²) is assigned a sound level of 30 db. A sound which is 10*10*10*10 or 10000 times more intense ( 1*10^-8 W/m²) is assigned a sound level of 40 db. Observe that this scale is based on powers or multiples of 10. If one sound is 10^x times more intense than another sound, then it has a sound level which is 10*x more decibels than the less intense sound. The human ear is sensitve over the range of 0-120 dB.

It is often termed the relative intensity level as it is a measure of relative intensity compared to a reference level. It is measured in decibels (dB).
b = 10 log (I/I_o).
Where I is the intensity of the sound in W m^-2,
I_o is taken as the threshold of hearing (10^-12 W m^-2).

The table below lists some common sounds with an estimate of their intensity and decibel level.

Distance	Intensity
1 m	160 units
2 m	40 units
3 m	17.8 units
4 m	10 units

Source	Intensity	Intensity Level	# Times Greater Than TOH
Threshold of Hearing (TOH)	1*10^-12 W/m²	0 dB	10⁰
Rustling Leaves	1*10^-11 W/m²	10 dB	10¹
Whisper	1*10^-10 W/m²	20 dB	10²
Normal Conversation	1*10^-6 W/m²	60 dB	10⁶
Busy Street Traffic	1*10^-5 W/m²	70 dB	10⁷
Vacuum Cleaner	1*10^-4 W/m²	80 dB	10⁸
Large Orchestra	6.3*10^-3 W/m²	98 dB	10^9.8
Walkman at Maximum Level	1*10^-2 W/m²	100 dB	10¹⁰
Front Rows of Rock Concert	1*10^-1 W/m²	110 dB	10¹¹
Threshold of Pain	1*10¹ W/m²	130 dB	10¹³
Military Jet Takeoff	1*10² W/m²	140 dB	10¹⁴
Instant Perforation of Eardrum	1*10⁴ W/m²	160 dB	10¹⁶