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Loudness

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The radio is on and your favorite song begins to play. With so much noise around you, you cannot quite hear the chorus. You want to hear it better, of course, so you crank up the volume. A simple turn of the stereo’s dial and the beats start pumping. But how did turning the dial magically increase the loudness? It’s not so mysterious when you understand the concept of loudness.


Definition of Loudness Edit

Loudness, in basic terms, is a person’s impression of the strength of a sound. The person’s impression is influenced by two major factors. One is the properties of the noise’s sound wave (like the amplitude and frequency). The other influence is how the human ear perceives the sound’s pulse. Since loudness is somewhat of a subjective term, these two factors must be considered jointly in order to most accurately describe the strength of a sound.

Now we can return to the example of a radio getting louder. The sound coming out of the speakers is changed in relation to the air-pressure level. To change this level, the amplitude of the sound wave must be increased. Sound waves with greater amplitudes move our eardrums more, and we register this sensation as a higher volume. This is because the air-pressure level that travels from the speakers to your ears increases and the sound gets louder. For a more in depth analysis of sound waves, see the next section.

Sound Waves Edit

In order to understand the concept of loudness, you need to understand the concept of sound waves and sound in general. All sounds travel in waves. Waves are identifiable by their three attributes: wavelength, frequency, and amplitude.

  • Wavelength is what the name infers; it is how long a cycle or period of a wave lasts.
  • The frequency of a wave, which is measured in Hertz (Hz), is how often a wave occurs. The frequency determines the pitch of a sound.
  • Amplitude is measured in decibels (dB) and it determines the loudness of a sound. The wave's amplitude is the change in pressure as the sound wave passes by. If you increase the amplitude of a sound, you are making it louder, just as you do when you turn up the volume on the television.

For those who are familiar with trigonometry, you already know the basic structure of a sound wave. Basic sound waves are represented by the equation Y = A*SinX. “A” defines the amplitude and loudness. Here is the graph: http://content.bolt.com/uploads3/photo/3/8/6/3/3863/medium/1149970825904.jpg (This is an original image)


Calculating Loudness: Adding Sounds Edit

When a sound is added to another existing sound, the increase in the perceived loudness depends upon the frequency of the new sound in relation to the frequency of the original sound. Insight into this process can be obtained from the Place Theory of Pitch Perception. This theory states that a person’s assessment of the pitch of a sound depends upon each person’s ear, specifically the level or region of the basilar membrane of the cochlea, which is set into vibration by the sound waves.

When adding sounds, if the second sound is extensively different in pitch from the first, then the sounds do not compete for the same nerve endings on the basilar membrane of the inner ear. Adding a second sound of equal loudness, however, yields a total sound about twice as loud. If the two sounds are close together in frequency, then the apparent combined loudness is only slightly greater than either sound was when they were on their own. This condition leads to the commonly used rule of thumb for loudness addition, which will be examined later in this article. http://hyperphysics.phy-astr.gsu.edu/Hbase/sound/imgsou/loudadd.gif Image is from: [[1]]


Decibels, Phons, Sones, Oh My! Edit

There are multiple units of measuring loudness, and each is defined in its own way.

  • Decibel: A unit used to convey relative difference in power or intensity, usually between two acoustic or electric signals, equal to ten times the common logarithm of the ratio of the two levels.
  • Phon: A unit of perceived loudness, equal in number to the intensity in decibels of a 1,000-hertz tone judged to be as loud as the sound being measured.
  • Sone: A subjective unit of loudness, as perceived by a person with normal hearing, equal to the loudness of a pure tone having a frequency of 1,000 hertz at 40 decibels.

!!Important notes concerning the distinction between these three units: In general, two different 60 decibel sounds will not have the same loudness. This is because saying that two sounds have equal intensity is not the same thing as saying that they have equal loudness. Also, if a given sound is perceived to be as loud as a 60 dB sound at 1000 Hz, then it is said to have a loudness of 60 phons. Therefore, 60 phons means “as loud as a 60 dB, 1000 Hz tone”


Historical Background on The Perception of Sound Edit

Early research into the physiology of hearing was conducted by Hermann von Helmholtz, a German physician who enjoyed the study of physics and closely examined the function of both the eyes and ears. He theorized that the ear detected differences in pitch through the action of the cochlea, the snail-shaped organ of the inner ear. As a physicist he understood sound waves and their properties, such as frequency (pitch) and amplitude (loudness). He proposed that certain notes sounded pleasing together because their pitches had a mathematical relationship. He contended that the quality of a tone depended on the intensities of other pitches known as overtones which combine to give a sound a particular tone or timbre.

Hermann von Helmholtz: http://web.archive.org/web/20100623233322/http://webphysics.davidson.edu/faculty/dmb/soundRM/helmholtz.jpg (Image from: [[2]])

In 1857, Helmholtz proposed his resonance theory of hearing in which he suggested that the fibers along the basilar membrane of the cochlea were of different lengths and thus had their own natural vibration or frequency. When a sound of that same frequency entered the cochlea, that fiber would resonate and sense the sound. He also suggested that the cochlea's structure resonated at particular frequencies to enable both pitch and tone to be perceived.

Although many of Helmholtz's ideas were right, his grasp of what occurs inside the cochlea was incorrect. Many years later, Georg von Békésy, a Hungarian-American physicist, studied the cochlea by placing it in a fluid bath and thus could see in more detail what occurred. He also studied the cochlea indirectly by making mechanical models to observe what happened when the fluid in the cochlea begins to move. He found that vibrations transmitted to the fluid in the cochlea set up traveling waves in the basilar membrane. When the frequency (pitch) of the stimulus was increased, the section of sensed vibration moved toward the end of his model that was closest to the middle ear. When the frequency was decreased, the section of sensed vibration moved toward the inner ear. For his work on physiological acoustics, Békésy was awarded the Nobel Prize in medicine or physiology in 1961, the first time a physicist ever won in that category.

Georg von Békésy: http://www.nobel-prize.org/EN/Medicine/images/bekesy.jpg (Image from: [[3]])

The understanding of the function of the inner ear, particularly the cochlea, has undergone a revolution in the last two decades. For example, scientists had believed that the cochlear tuning process was passive and mechanical. However, recent studies have shown that one group of cochlear hair cells have an active motion that enhances hearing. Research focused on the physiology of acoustics also laid the ground work for such advances as hearing aids and the cochlear implant, which involves surgically implanting electrodes in the cochlea to help stimulate the nerves involved in hearing. The implant helps people with hearing defects due to injury or loss of cochlear hair cells, which accounts for the most incurable forms of deafness.


Helpful Rule Of ThumbEdit

A widely used “rule of thumb” for measuring the loudness of a particular sound is to recognize that the sound’s intensity must be increased by 10 times for the sound to be perceived as twice as loud. For example, this rule states that it takes 10 tubas to sound twice as loud as 1 tuba. Another way to assert this rule is to say that the loudness doubles for every 10 phon increase in the sound’s loudness level. Although this rule is widely used, it must be stressed that it is an approximate, general statement. Whiel it is based upon a vast amount of information obtained when investigating the average human hearing, it is not to be taken as a set and absolute rule.

Visual representation of increasing loudness twofold: http://content.bolt.com/uploads3/photo/3/8/6/3/3863/medium/1149970921171.jpg (This is an original image)

One important restriction when using this “rule of thumb” for loudness is that it can only be used when adding loudness for identical sounds. If a second sound is too different from the first, then this rule is not applicable.


Practice Makes PerfectEdit

1. An electric guitar is generating a sound of constant frequency. An increase in which sound wave characteristic would result in an increase in loudness?

(1) speed

(2) period

(3) wavelength

(4) amplitude


2. An electric bell connected to a battery is sealed inside a large jar. What happens as the air is removed from the jar?

(1) The electric circuit stops working because electromagnetic radiation can not travel through a vacuum.

(2) The bell’s pitch decreases because the frequency of the sound waves is lower in a vacuum than in air.

(3) The bell’s loudness increases because of decreased air resistance.

(4) The bell’s loudness decreases because sound waves can not travel through a vacuum.


3. The diagram below shows two points, A and B, on a wave train. How many wavelengths separate point A and point B? http://online.cctt.org/physicslab/content/NYregents/2002Regents/August/images/Q17.gif

(1) 1.0

(2) 1.5

(3) 3.0

(4) 0.75



Answers: 1.(4), 2.(4), 3.(2)


References and Resources Edit

(follow hyperlink directly to site)


August 2002 Regents [[4]]

June 2004 Regents [[5]]

Loudness [[6]]

Phons [[7]]

Perception of Loudness [[8]]

Decibel [[9]]

Acoustics, Physiological [[10]]

Lazar, Miriam A. and Albert S. Tarendash. Barron's Review Course Series, Let's Review Physics. New York: Barron's Educational Series, Inc., 1996.

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