Sound is produced when something vibrates. The vibrating body causes the medium (water, air, etc.) around it to vibrate. Vibrations in air are called traveling longitudinal waves, which we can hear. Sound waves consist of areas of high and low pressure called compressions and rarefactions, respectively. Shown in the diagram below is a traveling wave. The shaded bar above it represents the varying pressure of the wave. Lighter areas are low pressure (rarefactions) and darker areas are high pressure (compressions). One wavelength of the wave is highlighted in red. This pattern repeats indefinitely. The wavelength of voice is about one meter long. The wavelength and the speed of the wave determine the pitch, or frequency of the sound. Wavelength, frequency, and speed are related by the equation speed = frequency * wavelength. Since sound travels at 343 meters per second at standard temperature and pressure (STP), speed is a constant. Thus, frequency is determined by speed / wavelength. The longer the wavelength, the lower the pitch. The 'height' of the wave is its amplitude. The amplitude determines how loud a sound will be. Greater amplitude means the sound will be louder.
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When two waves meet, there can be two kinds of interference patterns; constructive and destructive. Constructive inteference is when two waveforms are added together. The peaks add with the peaks, and the troughs add with the troughs, creating a louder sound. Destructive interference occurs when two waves are out of phase (the peaks on one line up with troughs on the other). In this, the peaks cancel out the troughs, creating a diminished waveform. For example, if two waveforms that are exactly the same are added, the amplitude doubles, but when two opposite waveforms are added, they cancel out, leaving silence.
Vibration inside a tube forms a standing wave. A standing wave is the result of the wave reflecting off the end of the tube (whether closed or open) and interfering with itself. When sound is produced in an instrument by blowing it, only the waves that will fit in the tube resonate, while other frequencies are lost. The longest wave that can fit in the tube is the fundamental, while other waves that fit are overtones. Overtones are multiples of the fundamental. The areas of highest vibration are called antinodes (labeled 'A' on the diagram), while the areas of least vibration are called nodes (labeled 'N' in the diagram). In an open pipe, the ends are antinodes. However, in a pipe closed at one end, the closed end is a node, while the blown end is an antinode. Thus, closed pipes yield only half the harmonics.
If a string that is fixed on both ends is bowed or plucked, such as in a violin, vibrations are formed that are in a standing wave pattern, having nodes at the fixed ends, and an antinode in the center. Several harmonics are also produced, in a similar way to the standing wave.
Overtones are the other frequencies besides the fundamental that exist in musical instruments. Instruments of different shapes and actions produce different overtones. The overtones combine to form the characteristic sound of the instrument. For example, both the waves below are the same frequency, and therefore the same note. But their overtones are different, and therefore their sounds are different. Note that the violin's jagged waveform produces a sharper sound, while the smooth waveform of the piano produces a purer sound, closer to a sine wave. Click on each wave to hear what it sounds like. Keep in mind that all are playing the same note.
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To help understand how sound works, download MouSing. It's a software theremin: an electronic instrument that allows direct control of pitch and amplitude. By moving your mouse horizontally across the screen, you alter the wavelength of the sound being produced, and thus the pitch (displayed in Hz on the bottom of the program). The higher the frequency, the higher the pitch. By moving the mouse vertically, you alter the volume, or amplitude, of the wave.