**Frequency, Wavelength, and Propagation Speed**

The purest acoustic signal is that of a sine wave of frequency* f* . This corresponds to air density and pressure at a single point increasing and decreasing at regular intervals. When the pressure is above the ambient (or quiescent) value, the density also increases, as a result of the air molecules being compressed together. The pressure then falls to a value below the quiescent pressure, with a corresponding decrease in the density as the result of the air molecules moving away from each other (show image of molecules undergoing alternating compressions and rarefactions).

- Frequency
*f**hertz*(1 Hz = 1 cycle per second). The frequency is also denoted by the radial frequency w = 2p*f*, expressed in radians per second.

- The period
*T*is the length of time for a single cycle to occur, and it is simply the reciprocal of*f*.

- If the frequency lies between 20 Hz and 20 kHz, the sound can be heard by humans. (Demonstration how the pitch varies with frequencies). This constitutes the audio frequency range. Below 20 Hz, sound is considered to be
*infrasonic*.*Ultrasonic*signals occurs above 20 kHz and cannot be heard by humans. Ultrasound finds a great deal of use in the medical field for both diagnostic and therapeutic purposes. In industry, it is used to clean materials, welding, detecting structural flaws (a major non-destructive test), serving as detector of intrusions.

- The
*wavelength*l constitutes the distance from one point in the cycle to the corresponding point in the next cycle. The vibrating molecules that transmit the acoustic signals do not, on the average.change their positions but merely move back and forth under the influence of the transmitted waves. The distances these particles move about their respective equilibrium positions are referred to as displacement amplitudes. The velocity at which the molecules oscillate back and forth are referred to as*particle velocity*, which is not to be confused with the*speed of sound c*which describes the rate the acoustic waves travel through a medium.

- Frequency, wavelength and propagation speed are related to each other by the relation:

- The speed of sound for an ideal gas may be found from

where g is the ratio of specific heats, which is equal to 1.4 for air, p the absolute pressure, r the mass density, *R* the thermodynamic gas constant, and *T* the absolute temperature of the gas.

- The speed of sound in an elastic solid may be predicted from:

where* E* is the elastic constant for the solid and r the mass density of the solid.

- The speed of sound in a liquid does not lend itself to simple expressions. Experimental measurements need to be conducted to determine propagation speeds in liquids as function of the mediumâs temperature and, to a lesser degree, pressure.

- Sound propagation speed in gases are lower than those in liquids. And sound travels more swiftly in solids than in liquids. For instance, the velocity of sound in dry air at 20¼C is 344 m/s; that for propagation through water 1500 m/s, and that for steel 5140 m/s.

Return to the Overview of Acoustics and its Applications in Medical Fields

Move back to Sources of Acoustic Signals

Move forward to Basic Wave Equations and Solutions

Support for the development of this module was provided by the National Science Foundation and The Cooper Union for the Advancement of Science and Art.

Please send questions or comments to Professor Ron Adrezin or Professor Daniel Raichel.