Thursday, September 27, 2007

Sound, waves and frequencies


Sound is a very basic element in our lives. Sounds are all around us, falling trees, trucks honking, dogs barking and countless others which we don’t even hear. But what is sound anyway?

Any sound, whatever it might be, is caused by something vibrating. Without vibration there can be no sound. The vibrating body causes the air particles next to it to vibrate; those air particles, in turn, cause the particles next to them to vibrate. In this way a disturbance of the air moves out from the source of the sound and may eventually reach the ears of a listener. This disturbance causes our ear drums to vibrate and our brains pick up the sound that we hear.

The sounds we hear are propagated in the air which is a transmission medium. Sound can travel in other mediums as well (as long as the medium has some particles to vibrate) like water, glass and buildings.

The sound travels in the medium in the form of waves. For example when you throw a stone in a pond or river, you would see circular waves moving out from the place where stone touched the water.

So what is a wave then?

A wave represents the periodic motion (vibration) of an object or particles in a medium. It describes the pattern in which an object vibrates. Since the vibrations can happen in any form, a wave can be of arbitrary shape. Following figure shows some example of waveforms

Sine Wave
Saw Tooth
Square wave
Zigzag

Wave which is periodic in nature i.e. where the movement of particles has a definite pattern can be described by mathematical formulae. For example the Sine Wave can be described by a function

Each wave irrespective of its shape has certain common characteristics

Amplitude – The maximum displacement of the particle from its mean position.

Cycle – Each complete vibration is called a cycle. From its starting position, to a maximum distance in one direction, back through the starting position, then to a maximum displacement in the opposite direction and back to the starting place

Frequency – No of cycles in one second is called frequency of the wave and measured in Hz (Hertz). (One thousand hertz = 1 kilohertz = 1 kHz.)

For example the frequencies of notes that can be played on a piano range from 27.5 Hz to just over 4kHz.

Pitch – Pitch is a subjective quality, often described as highness or lowness, and is something perceived by the human ear only. For example the sound produced from a drum has lower pitch than the sound produced by a whistle. Usually it is related to the frequency and amplitude of the sound but not always.

Tone – Sound consisting of a single wave of fixed frequency is usually referred to as tone or “pure tone”.

Harmonics- Most of the musical instruments (for example Guitar, when a string is plucked) generate more than one wave of different frequencies (sounding all together) which are related to each other. These frequencies are related to the frequency (usually to the lowest one) which gives the sound its characteristic pitch.

The tone with the lowest frequency is called the fundamental. The other tones are called overtones If the overtones have frequencies that are whole number multiples (x2, x3...up to x14) of the fundamental frequency they are called harmonics. It is the difference in the harmonic content of notes that gives each musical instrument its characteristic sound or timbre ("tam-brah").

Sound intensity or Loudness - It is the strength (or loudness) of the sound that we hear. For example an airplane sounds much louder than the sound of a car.

Sound loudness is a subjective term describing the strength of the ear's perception of a sound. It is intimately related to sound intensity but can by no means be considered identical to intensity. The intensity of the sound is measured in Decibels (db). Decibel scale is a logarithmic scale and not a linear scale.

The sound intensity also depends on the distance of the source from the listener as the sound waves loose strength (energy) when traveling in air.
Musical Note
What we perceive a musical note is subject to our interpretation. Any sound which is pleasant in nature can be called a musical note. Musical notes have been defined as sounds which are smooth, regular, pleasant and of definite pitch, and unmusical sounds have been those which are rough, irregular, unpleasant and of no definite pitch.

Usually it is the presence of harmonics in the sound which makes it pleasant. That is why musical instruments (such as guitar or violin) sound pleasant. The sound produced by these instruments contains a fundamental frequency tone and lot of other overtones.

A musical instrument such as piano is capable of producing a range of musical notes. Pressing a particular key of piano produces a musical note (sound) consisting of tone and overtones of a definite frequencies. Pressing other key would produce another musical note which has different frequencies sounding totally different from previous musical note.

It is important to note that frequencies of the tones produced by two different piano keys are still related with each other.

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