Wavelength, Frequency & Pitch..

 

The aspect of evenly spaced waves that really affects music theory is the spacing between the waves, the distance between one high point and the next.  This is the wavelength and it affect the pitch of the sound.  The closer together the waves, the higher the sound.  all waves are traveling at about the same speed, the speed of sound.  So waves with a shorter wavelength arrive at your ear more often (frequently) than longer waves.  This aspect of sound is called Frequency by scientists and engineers.  They measure it in Hertz, which is how many peaks go by per second.  People can hear sound from about 20 - 17,000 hertz.

The word musicians use for frequency is Pitch.  The shorter the wavelength, the higher the frequency, the higher the pitch.  Instead of using frequencies, musicians use notes.  Most tuning is from A-440 standard.  That means the note A is at 440 hertz.  Other than A-440 musicians only use note names to describe frequencies.

Standing Waves and Musical Instruments:

Musical tones are produced by musical instruments or the human voice.  So the physics of music is the physics of the kinds of sounds these instruments can make.  What kinds of sounds are these?  They are tones caused by standing waves produces in or on an instrument.  So the properties of these standing waves have far reaching effects on music theory.  Most sound waves, including musical instruments are not standing waves.  Normally when something makes a wave it travels outward until it reaches something, it can bounce (reflection) or be bent (refraction).  In fact you can trap waves by making them bounce back and forth between two or more surfaces.  Musical instruments produce pitches by trapping sound waves.

Why are trapped waves useful for music?  Musical instruments are able to arrange the trapped waves in a way that the new waves reinforce the existing waves instead of canceling them out.   So musical instruments are basically sound wave containers.  The two most common containers are strings and hollow tubes.  So, what makes a good standing wave container?

In order to get the necessary constant reinforcement, the container has to be the perfect size (length) for a certain wavelength so that the waves bouncing back and forth reinforce each other instead of interfering.  If you were to watch these waves it would appear that they were appearing and disappearing in the exact same spot, so these trapped waves are called standing waves.

Notice that it does not matter what the length of the fundamental is, the waves in the second harmonic must be half the length, the third harmonic a third the length etc.  This has a direct effect on the frequency and pitch of harmonics and so it affects the basics of music tremendously.

All standing waves have places called nodes where there is no wave motion and antinodes where the wave is the largest.  It is the placement of the nodes that determine which wavelengths fit into a musical instrument container.

One container that produces standing waves very well is a thin, very taut string that is held tightly at both ends.  Since the string is taut, it vibrates quickly producing sound waves if you pluck it or rub it with a bow.

The fundamental wave is the one that gives the string its pitch.  The other vibrations (the ones that divide the wave in half, thirds etc.) produce a whole series of harmonics.  We do not hear the harmonics as individual notes but rather as a whole that give each musical instrument its own unique sound.