Colorado College OVAL Project

page prepared on April 10, 2001

Some Basic Concepts Related to Sound

What is SOUND? -- compressional wave in a medium such as air or water -- a medium is required so that pressure can build up and relax over and over again (no sound out in space) --

What is a WAVE? -- A wave repeats itself over and over again at any one point and moves from one location to another. At one point the wave has an amplitude that increases and decreases with some frequency (cycles per second). Taking a snapshot of the wave at one instant in time shows the amplitude changing smoothly from maximum to minimum over a distance termed the wavelength. Watching the wave propagate along we find that the speed of the wave equals the product of the frequency times the wavelength. (speed = distance of one wavelength / time for one oscillation [i.e. seconds per cycle])

What causes the FREQUENCY of a sound? Sounds are created by rapidly pushing back and forth on the medium (air or water) that will then carry the sound. In our voice-box, muscles and tissues vibrate and this motion compresses and expands the air starting the sound wave on its way. If we strike something with a hammer, this object will respond by vibrating and again, this vibration will push on the medium and the sound wave will move away vibrating at the same frequency as the material whose vibration first created this sound. This implies that when a sound moves from air to water or vice versa, the frequency of the sound will be the same in each medium.

What causes the SPEED of a sound wave? When a sound starts on its way, the molecules near the vibrating source of the sound are momentarily forced close together. A moment later these nearby molecules spring apart and in doing so push on molecules slightly farther away, pushing those closer together. This process continues and the sound wave propagates away from the original source of the vibrations. In air, molecules have to move a considerable distance before they are likely to hit an adjacent molecule and this takes a bit of time. The speed of sound in air is about 330 meters per second. In contrast, in liquid water, molecules are shoulder to shoulder touching one another and hence the time it takes for one molecule to influence its neighbor is much less than in air. The result is that the speed of sound in water is about five times that in air (typically 1500 meters per second). In summary, if a sound moves from air to water or vice-versa, its wavelength will change, becoming about five times longer in water than in air. If we change the density of the medium (air or water) we will change the speed of sound. For example, increasing the temperature will speed up the random motion of the molecules in our medium, and as the molecules are moving faster, any sound wave will propagate faster. Similarly, increasing the pressure or the salinity of water increases the density and hence increases the speed of sound.

What causes the AMPLITUDE of a sound wave? The harder we push initially to start the sound wave, the larger the amplitude of the resulting pressure wave. As a sound wave propagates away from its source, the wave spreads the initial energy out over a larger and larger region. (The energy in a wave is proportional to the square of the amplitude of the pressure of the wave.) Hence the amplitude of the wave received from a distant source will be much smaller than when listening close to the source. Our ears are able to hear sounds whose volumes or loudness vary over a tremendous range. The pressure of the loudest sound that we can withstand without permanent hearing damage is one million times that of the softest sound that the human ear can discern. Because of the square relationship between pressure and energy, the energy range between these two limits is more than one trillion!

What is a DECIBEL? A nonlinear (logarithmic) measure called the decibel is used to quantify sounds over this extensive range of pressures. Different definitions of the decibel (dB) are used for sounds in air versus sounds in water. The SOUND PRESSURE LEVEL in decibels is defined as 20 log (pressure/reference pressure), using base 10 logarithms. Usually the pressure refered to here is the "root mean square" average pressure (abreviated as rms). The loudness or intensity of a sound is proportional to the square of the rms average pressure that the molecules exert on their neighbors as the wave propagates. Hence, the loudness of a sound in decibels can also be defined as 10 log (intensity/reference intensity). The reference pressure for sound waves in water is taken to be 1 microPascal while in air, the reference pressure used is 20 microPascals.

What FREQUENCY RANGE is important? Humans can hear sounds with frequencies from as low as 20 cycles per second (Hz) to as high as 20,000 Hz. Most of what we hear is within the frequency range from a few hundred hertz to a few thousand. Orca whales emit sounds that have most of their energy in this range of common human hearing. Other whales and porpoises emit sounds that may be much, much lower or much, much higher in frequency than typical Orca calls.

What is meant by SOURCE LEVEL as compared with RECEIVE LEVEL? By definition, the strength of a sound source, the SOURCE LEVEL, is defined as the sound pressure level (also loudness, intensity, energy), in decibels, of the source at one meter from the source. (We make the assumption that the source can be thought of as a tiny point source from which sound spreads out over a sphere of radius one meter.) As a sound spreads out from its source, its intensity decreases as the energy is spread over larger areas. At any distance, other than the reference one meter distance, the sound pressure level (dB) is called the RECEIVE LEVEL.

Where does SOUND ENERGY go? As a sound wave moves along, its loudness or volume decreases as its energy is spread out over a larger and larger domain. For a wave spreading out equally in all directions (spherical symmetry), the loudness of the wave dimishes rapidly. In a uniform medium, the the sound energy is spread over a sphere that gets larger and larger as the wave moves away from its source. This is called SPHERICAL SPREADING. In this case, the loudness (the energy flow divided by the area) decreases in proportion to the square of the distance from the source. In decibels, the received level is equal to the source level minus 20 log(R) where R is the distance from the source to the receiver in meters. For example, the energy of a sound wave at one kilometer is one millionth of the energy at one meter. In decibels, this is 60 dB less than the sound pressure level at one meter from the sound source. (Since the loudness of proportional to the square of the pressure in the sound wave, a 60 dB drop in loudness corresponds to a decrease in pressure by a factor of one thousand.) In addition, a small portion of the energy of a sound wave is lost from the wave as some of the molecular motion that creates the sound pressure waves is converted into random molecular motion (heat). Sound absorption in the ocean is very small and is strongly frequency dependent. At 100 Hz a sound wave can go 1000 kilometers and only suffer only a 1 dB loss in intensity. Such low frequency sounds can propagate all the way across an ocean with very little absorption of energy. At 1000 Hz this same 1 dB loss occurs in a distance of only 1 km. In the range of common human hearing, absorption of sound in ocean water is much less important than is the weakening of sound energy due to the geometric spreading of waves as they leave their source. When sound energy reaches one of the edges of its medium (surface of the ocean, bottom of the ocean, shore of the ocean) some of its energy is reflected, some is transmitted across the boundary, and some is converted into heat.

What PATHS do sound waves take from their source to a listener? Sounds generally take a straight-line path from a source of sound to an observer some distance away. This path (being the shortest) will generally take the least time for a sound wave to move from its source to a receiver. Sound waves may also bounce off the bottom of the sea or off the top surface of the ocean and reach a listener after one or more such reflections. In such situations the listener will hear a whole series of copies of the original sound each displaced a bit in time. This tends to spread out or smear the clarity of the original sound. If the speed of sound changes, typically with depth as pressure, temperature and/or salinity changes, sound waves will bend smoothly as that portion of a wave that reaches a faster sound region moves away from portions of the wave that are still in a slower medium. This process is called refraction. Sound waves can become trapped in regions that have slower sound velocities. In such channels, sounds can be detected traveling across entire ocean basins.

In SHALLOW WATER, after a sound wave has traveled some distance from its source, the processes of reflection off the surface of the water and off the bottom traps the sound between these two interfaces. In this situation the loudness or intensity (the energy flowing outward per unit area) does not decrease as fast as in the spherical spreading (deep water) case. Here sound tends to move outward along a cylindrical surface center on the sound source and hence loudness decreases in proportion to the distance (here we are assuming that absorption in the water and transmission into the air or seabottom are insignificant). This is called CYLINDRICAL SPREADING and the sound pressure level drops from the source to the receiver by -10 log(R) where R is 1 meter at the source and R meters at the receiver.

What SOURCES are there for sounds in Puget Sound? Human generated sounds in Puget Sound emanate from ships of all sizes. (Container ships, tankers, barges, whale-watch boats, outboard motors .....) Natural sounds are created by Orca whales, other sea mammals, rain, breaking waves, ....

How can we determine WHERE these sources are? Humans use their two ears to locate the position of sound sources. Our brains determine which ear first receives a sound wave and then tells us whether the sound is to our left or right. More subtle signal processing gives us an idea as to whether the sound source is above or below. Hydrophones placed in the water in Puget Sound can tell us the same thing for sources of sound in the ocean.