Natural Frequency and Sound
This activity investigates sounds produced in accordance with the natural frequencies of objects we use in everyday life. It also studies the characteristics of frequencies.
Theory
Hitting, striking, plucking, or otherwise disturbing just about any object will cause it to vibrate. Dropping a pencil or ruler to the floor, or plucking a banjo string will cause it to vibrate. The sound produced when you blow over the top of a bottle is the air inside of it vibrating. The vibration of an object tends to occur at a particular frequency or a particular set of frequencies, which is the “natural frequency” of the object.
Though the strength of the strike, pluck, or other disturbance applied to an object affects the frequency of the sound produced, in most cases the sound produced is a louder version of the natural frequency. Generally, the sound produced by an object is the result of multiple natural frequency sound waves superimposed on each other.
The expression below provides the natural frequency of a string that is fixed at both ends. In this case, all of the natural frequencies are integer multiples of f1, which is called the “fundamental frequency.” The fundamental frequency is the lowest possible frequency at which an object can vibrate freely.
fn = | n |
|
| S |
|
| ρ | ||||
2 L | |||||
fn (Hz) | : String Natural Frequency (n = 1, 2, 3 ...) | ||||
L (m) |
| : String Length | |||
S (N) |
| : String Tension | |||
ρ(kg/m) : String Linear Density (per meter)
English
Activity:tivity: SetupSetup
Equipment
BoxString Bolts (2)Triangular Wood Blocks (2)
Audio Measurement Setup
Building a Monochord
uUse tape to affix the bolts at either end of the box, and stretch the string taut between them.
uInsert a triangular wood block between the string and the box.
1Box
2Box Length: 50cm
3Bolt
4String
5Block
Setting Up
uInsert two wood blocks between the string and box, and set the monochord on a table or desk.
uPosition the Audio Measurement Setup where it can pick up the sound from the monochord.
1Desk
2Monochord
3
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