Sound is a longitudinal wave transmitted by the oscillation of particles in a deformable medium.1 Sound needs a medium which contains particles. As such, sound can travel through solids, liquids, and gases, but cannot travel through a vacuum. The speed of sound is fastest in a solid with low density, and slowest in a very dense gas. The speed of sound in air at 20°C is approximately 343 m/s. Sound is produced by the mechanical disturbance of particles in a material along the sound wave’s direction of movement. Although the particles themselves do not travel along with the wave, they do vibrate or oscillate about an equilibrium position, which causes small regions of compression to alternate with small regions of decompression. These alternating regions of increased and decreased particle density travel through the material, allowing the sound wave to propagate.1 Since sound involves vibration of material particles, the source of any sound is ultimately a mechanical vibration of some frequency. They can be produced by the vibration of solid objects or the vibration of fluids, including gases. Solid objects that can vibrate to produce musical sound include strings and metal (bells). Vibration of air within certain objects, including all woodwinds and brass instruments, pipe organs, and even a soda bottle, can also create musical sound. The frequency at which the air column within the instrument vibrates is determined by the length of the air column, which can be changed either by covering holes in the instrument or directly changing its length. Sound is created by passing air between the vocal cords, which are a pair of thin membranes stretched across the larynx. As the air moves past the cords, they vibrate causing the air to vibrate at the same frequency. The pitch of the sound is controlled by varying the tension of the cords. Adult male vocal cords are larger and thicker than those of adult females; thus, the male voice is typically lower in pitch.
The loudness or volume of a sound is the way in which we perceive its intensity.1 Perception of loudness is subjective, and depends not only on brain function, but also physical factors such as obstruction of the ear canal, stiffening of the ossicles, or damage to cochlear hair cells by exposure to loud noises or with age. Sound intensity, on the other hand, is objectively measurable. Intensity is the average rate of energy transfer per area across a surface that is perpendicular to the wave. In other words, intensity is the power transported per unit area. The SI units of intensity are therefore watts per square meter (W/m2). Intensity is calculated using the equation:
I = P/A
where P is the power and A is the area. Rearranging this equation, we could consider that the power delivered across a surface, such as the tympanic membrane (eardrum), is equal to the product of the intensity I and the surface area A, assuming the intensity is uniformly distributed. The amplitude of a sound wave and its intensity are also related to each other: intensity is proportional to the square of the amplitude. Therefore, doubling the amplitude produces a sound wave that has four times the intensity. Intensity is also related to the distance from the source of the sound wave. As sound waves emanate outward from their source, it is as though the waves are pushing against the interior wall of an ever-expanding spherical balloon. Because the surface area of a sphere increases as a function of the square of the radius (A = 4πr2), sound waves transmit their power over larger and larger areas the farther from the source they travel. Intensity, therefore, is inversely proportional to the square of the distance from the source. For example, sound waves that have traveled 2 meters from their source have spread their energy out over a surface area that is four times larger than that for identical sound waves that have traveled 1 meter from their source. The softest sound that the average human ear can hear has an intensity equal to about 1 x 10-12 W/m2. The mechanical disturbance associated with the threshold of hearing is remarkably small, the displacement of air particles is on the order of one billionth of a centimeter. At the other end of the spectrum, the intensity of sound at the threshold of pain is 10 W/m2. The intensity that causes instant perforation of the eardrum is approximately 1 x 104 W/m2. This is a huge range, which would be unmanageable to express on a linear scale. To make this range easier to work with, we use a logarithmic scale, called the sound level (β), measured in decibels (dB):
β =10 log (I/I0)
where I is the intensity of the sound wave and I0 is the threshold of hearing (1 x 10-12 W/m2). When the intensity of a sound is changed by some factor, one can calculate the new sound level by using the equation:
βf = βi + 10 log (If/Ii)
where (If/Ii) is the ratio of the final intensity to the initial intensity.
Sound is not transmitted undiminished. Even after the decrease in intensity associated with distance, real world measurements of sound will be lower than those expected from calculations. This is a result of damping, or attenuation. Oscillations are a form of repeated linear motion, so sound is subject to the same non-conservative forces as any other system, including friction, air resistance, and viscous drag. The presence of a non-conservative force causes the system to decrease in amplitude during each oscillation. Because amplitude, intensity, and sound level (loudness) are related, there is a corresponding gradual loss of sound. Note that damping does not have an effect on the frequency of the wave, so the pitch will not change. This phenomenon, along with reflection, explains why it is more difficult to hear in a confined or cluttered space than in an empty room: friction from the surfaces of the objects in the room actually decreases the sound waves’ amplitudes. Over small distances, attenuation is usually negligible.
When an ambulance with its sirens blaring quickly approaches from the other lane, as it passes, one can hear a distinct drop in the pitch of the siren. This phenomenon affecting frequency is called the Doppler effect, which describes the difference between the actual frequency of a sound and its perceived frequency when the source of the sound and the sound’s detector are moving relative to one another.2 If the source and detector are moving toward each other, the perceived frequency, f′, is greater than the actual frequency, f. If the source and detector are moving away from each other, the perceived frequency is less than the actual frequency. This can be seen from the Doppler effect equation:
where f′ is the perceived frequency, f is the actual emitted frequency, ν is the speed of sound in the medium, νD is the speed of the detector, and νS is the speed of the source. When using this formula, the upper sign should be used when the detector or source is moving toward the other object. The lower sign should be used when the detector or source is moving away from the other object. The Doppler effect applies to all waves, including light.2 This means that if a source of light is moving toward the detector, the observed frequency will increase. This is called blue shift because blue is at the high-frequency end of the visible spectrum. If the source is moving away from the detector, the observed frequency will decrease, causing red shift.
Frequency is the rate at which a particle or wave completes a cycle. Human perception of that frequency of sound is called the pitch. Sound frequencies within the normal range of human hearing, ranges from 20 Hz to 20,000 Hz. Sound waves with frequencies below 20 Hz are called infrasonic waves, and those with frequencies above 20,000 Hz are called ultrasonic waves.
Ultrasound uses high frequency sound waves outside the range of human hearing to compare the relative densities of tissues in the body. An ultrasound machine consists of a transmitter that generates a pressure gradient, which also functions as a receiver that processes the reflected sound. Because the speed of the wave and travel time is known, the machine can generate a graphical representation of borders and edges within the body by calculating the traversed distance. Note that ultrasound ultimately relies on reflection; thus, an interface between two objects is necessary to visualize anything. Ultrasound can also be used therapeutically. Ultrasound waves create friction and heat when they act on tissues, which can increase blood flow to a site of injury in deep tissues and promote faster healing. Focused ultrasound also has a range of applications. Focusing a sound wave using a parabolic mirror causes constructive interference at the focal point of the mirror. This creates a very high-energy wave exactly at that point, which can be used to noninvasively break up a kidney stone or destroy small tumors. Ultrasound can also be used for dental cleaning and destruction of cataracts. In each case, the ultrasound waves are applied for a sufficient time period to achieve the desired effect.
In a special case of the Doppler effect, an object that is producing sound while traveling at or above the speed of sound allows wave fronts to build upon one another at the front of the object. This creates a much larger amplitude at that point. Because amplitude for sound waves is related to the degree of compression of the medium, this creates a large pressure differential or pressure gradient. This highly condensed wave front is called a shock wave, and it can cause physical disturbances as it passes through other objects. The passing of a shock wave creates a very high pressure, followed by a very low pressure, which is responsible for the phenomenon known as a sonic boom. Unlike its depiction in movies and television, a sonic boom can be heard any time that an object traveling at or faster than the speed of sound passes a detector, not just at the point that the speed of sound is exceeded (Mach 1). Once an object moves faster than the speed of sound, some of the effects of the shock wave are mitigated because all of the wave fronts will trail behind the object, destructively interfering with each other.
1) Handel, S. (1995). Timbre perception and auditory object identiﬁcation. Hearing, 425-461.
2) Strutt (Lord Rayleigh), John William (1896). MacMillan & Co, ed. The Theory of Sound. 2 (2 ed.). p. 154.
3) Halliday, David; Resnick, Robert; Walker, Jerl (2005), Fundamental of Physics (7th ed.), USA: John Wiley and Sons, Inc.,
4) James D. Ingle, Jr. and Stanley R. Crouch, Spectrochemical Analysis, Prentice Hall, 1988
5) Lekner, John (1987). Theory of Reflection, of Electromagnetic and Particle Waves. Springer.
6) Hecht, Eugene (1987). “5.4.3”. Optics (2nd ed.). Addison Wesley. pp. 160–1