Much of what we know about music and how tension, length, and thickness affect the frequency of vibrating strings can be accredited to the Greek philosopher Pythagoras. He discovered that if one string vibrates with twice the frequency of an identical string, we hear the higher frequency as once octave higher in pitch than the lower frequency. This can be demonstrated by playing the middle C on a piano, then the next C to the right. That pitch will be one octave higher because the second C will resonate with the middle C and increase its amplitude. Pythagoras also found that whole number ratios of frequencies produce sounds that are harmonious to the human ear. That is the reason we found the two different C notes on the piano to be pleasing to the ear. Even the musical scale is based on the frequency ratios of sound.
As we investigate musical instruments, we will discover that some type of vibrating system produces all musical sounds. The strings on the guitar, or the air column in the clarinet, and the head of the drum are examples of vibrating systems. The vibrating systems on most musical instrument are made up of two or more vibrating systems working together to produce sounds loud enough to be heard by the human ear. Examples of instruments with two or more vibrating systems include the membranes of leather stretched across the tensioning loop of a drumhead, the strings and the sounding board of a piano. Other examples are the strings and the body of a guitar or violin, or the reed and air column of the air column of the clarinet.
A vibrating string produces very little sound. Therefore, most string instruments have a sounding board. Your students can investigate how the sounding board increases the intensity of a sound by stretching a rubber band between your finger and thumb. Pluck the rubber band and describe the loudness of the sound. Then have the students place the same rubber band around a pie plate and pluck the rubber band. They will find that the sound of rubber band is much louder.
The sounding board on musical instruments increases sound in the exact same manner. The vibration made on the sounding board is called forced vibration because the natural frequency of the board usually does not match the frequency of the vibrating string. As the two frequencies match when the string is plucked, resonance amplifies the sound.
Wind instruments depend on the vibration of a column of air to produce sound. The column of air vibrates when wind is blown into or across an instrument. There are two types of wind instruments, brass and woodwind instruments. Brass instruments are played by vibrating the lips and pressing them against the mouthpiece of the instrument. This causes the air column to vibrate and create sound. Woodwind instruments such as the clarinet need a reed to make the air columns vibrate. The column of air vibrates in the flute and piccolo when air is blown across a hole. Higher or lower pitch can be produced in these instruments by making the air column shorter or longer.
Most percussion instruments produce sound when the material stretched over a hollow container vibrates when struck by a stick, mallet or hand. However, some percussion instruments are solid and vibrate when it is struck by another object. The piano is also considered a percussion instrument because the strings are set into motion or vibration by a hammer, which acts on the bridge of the piano, which cause the sounding board to vibrate. The percussive instruments produce pitch either by tightening the stretched material, or by using thinner or smaller pieces of material.