Sources of Sound
At the very basic level, something must vibrate in order for there to be sound. Have you ever seen a speaker cone vibrating back and forth as it is
operating? Remember, sound is a mechanical (requires a medium), longitudinal wave. The sounds we will talk about are going to come from
vibrating strings (pianos, guitars, and other stringed instruments as well as vibrations of high tension lines) or air columns (horns or organ pipes). Sounds are produced when the source is set into
resonance and a standing wave is produced. Let's start with a string. Plucking the string causes the string to vibrate at its fundamental
frequency. This is also called the first
harmonic. Harmonics are integral multiples of the fundamental frequency. For example, a frequency of 220 Hz has harmonics at 440Hz, 660 Hz, 880Hz, etc. We also use the term overtone to describe harmonics. A fundamental frequency is not considered to be an overtone. In this case, there is one standing wave on the sstring. The wavelength of the sound is twice the length of the string. Touching the string in the center can cause the formation of a node at that point and the string now resonates at its second harmonic or first overtone. Here, you can see one complete wavelength runs the length of the string. Forcing the string to resonate with yet another node as shown below places the string at its third harmonic or second overtone. The wavelength is 2/3 the length of the string. The pattern continues.
In fact, in any stringed instrument, the wavelength is given by the formula
where L is the length of the vibrating string and n is the number of the harmonic. (For more on strings, try http://www.phys.unsw.edu.au/~jw/strings.html)
Have you ever blown across the top of a bottle and gotten a sound? That is from setting up a standing wave iin an air column in the bottle. In a pipe where we are resonating a column of air to produce a sound, there are two different cases. The first case is a pipe that is open at both ends. Here, both ends of the pipe have antinodes (the air is vibrating with maximum displacement). All harmonics are possible with a pipe open at both ends, and, just like with a string, the formula for finding the wavelength of the various harmonics is
The second case is a pipe that is closed at one end. This is a little different, because we can only have a node at the closed end and an anti node at the open end. In this case, only odd harmonics (1st, 3rd, 5th, etc) can exist in the pipe. Our formula for finding the wavelength of these harmonics is
where n must be an odd number. Interestingly enough, closed end pipes can be half the length of an open end pipe to produce the same note. A pipe closed at both ends would not produce a sound - there is no source of air to vibrate. Of course, sounds come from other things as well. Anything that vibrates in the audible frequency range will produce a sound that we hear.
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