Musical Instruments And Wave Equation
Musical Instruments And Wave Equation
The wave equation determines what you hear when playing a musical instruments. For example, when you strike a guitar string, it vibrates to form a transverse wave.Whatever not you play on a particular string, the speed of the wave along that string in the same. By moving your finger along the frets you shorten the vibrating length of the string and therefore, the wavelength of the wave. As the wavelength decreases, the frequency of the note increases.
Place your finger on exactly the same fret but on a different sting and you get a note of a different frequency. This because different strings have different thicknesses, are made from different materials and are under different tensions. This combination of factors alters the speed of the wave that travels down then when struck. The wavelength might be the same but the speed is now different and so its frequency is different too.
Other stringed instruments such as violins and cellos work in the same way. Pianos and harps many strings of different lengths. Each string vibrates to form a particular wavelength and a particular frequency. When a woodwind or brass instrument such as a trombone is blown, a longitudinal compression wave is formed in the air inside the instrument. Increasing the length of the trombone causes the wavelength to increase.
As a result, the frequency of the wave produced decreases and a deeper note is heard. Many wind instruments such as recorders and clarinets do not physically alter the length of their instruments but instead let air escape through holes. When all the holes are closed, the full length of the instrument is used to form the wave. Opening a hole has the effect of shortening the length of the air column inside the instrument and the wavelength formed in it. As a result, the frequency of sound produced is increased and a higher note is heard.
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