FREQUENCY
Sounds can be produced at a desired frequency by different methods. Sirens emit sound by means of an air blast interrupted by a toothed wheel with 44 teeth. The wheel rotates at 10 revolutions per second to produce 440 interruptions in the air stream every second. Similarly, hitting the A above middle C on a piano causes a string to vibrate at 440 Hz (i.e., fundamental frequency). The sound of the speaker and that of the piano string at the same frequency are different in quality, but correspond closely in pitch. The next higher A on the piano, the note one octave above, has a frequency of 880 Hz, exactly twice as high. Similarly, the notes one and two octaves below have frequencies of 220 and 110 Hz, respectively. Thus, by definition, an octave is the interval between any two notes whose frequencies are in a two-to-one ratio (see figure 7.4).
Figure 7.4: Sound waves with different octaves (Reprinted from Encyclopedia Encarta 2004 © 1993-2003 Microsoft Corporation).
We perceive frequency as “higher” or “lower” sounds. In the figure above, the frequency of each higher wave is double that of the one below, producing the same note at different frequencies, from 110.00 Hz to 880.00 Hz. Waves propagate at both higher and lower frequencies, but humans are unable to hear them outside of a relatively narrow range (between 15 Hz and 20,000 Hz).
Frequencies of oscillating objects can cover a wide range of values. The tremors of earthquakes may have a frequency of less than one, while the rapid electromagnetic oscillations of gamma rays may have frequencies of 1020 or more. In almost all forms of mechanical vibration, a relationship exists between frequency and the physical dimensions of the vibrating object. Thus, for example, the time required by a pendulum to make one complete swing is partly determined by the length of the pendulum; the frequency or speed of vibration of a string of a musical instrument is partly determined by the length of the string. In each instance, the shorter the object, the higher the frequency of vibration.
In wave motion of all kinds, the frequency of the wave is usually given in terms of the number of wave crests that pass a given point in a second. The velocity of the wave and its frequency and wavelength are interrelated. The wavelength (the distance between successive wave crests) is inversely proportional to frequency and directly proportional to velocity.
Frequency is expressed in hertz (Hz); a frequency of one Hz means that there is one cycle or oscillation per second. The unit is named in honor of the German physicist Heinrich Rudolf Hertz, who first demonstrated the nature of electromagnetic wave propagation. Kilohertz (kHz), or thousands of cycles per second, megahertz (MHz), or millions of cycles per second, and gigahertz (GHz), or billions of cycles per second, are employed in describing certain high frequency phenomena, such as radio waves. Radio waves and other types of electromagnetic radiation may be characterized either by their wavelengths, or by their frequencies. Electromagnetic waves of extremely high frequencies, such as light and X rays, are usually described in terms of their wavelength measure, which is often expressed in angstrom units (symbolized as Å meaning hundred-millionths of a cm). An electromagnetic wave that has a wavelength of one Å has a frequency of about three billion GHz.
