Musical instruments
25 Natural frequency
Forced vibration
Why is it that some bridges have literally shaken apart in heavy wind? How is it that different strings on a guitar produce different pitch from the same pluck?
Objects can force other objects to vibrate. A mallet strikes a tuning fork. Wind rushes past a building or through the wires of a suspension bridge. Heavy machinery shakes the floor. The bow drags across a violin string. This is called forced vibration. What happens next depends not just on the force, but also on the properties of the system being driven.
Natural frequency
Many vibrating systems have a frequency at which they oscillate easily. A classic example is a person on a swing. Release yourself from some height and you will automatically swing back and forth at a certain frequency. It does not matter how high you start, or whether you pump your arms- the swing will always go back and forth with the same frequency. The swing-person system has a natural frequency– a preferred frequency of vibration. Some systems, like strings and air columns, have more than one natural frequency. That’s why musical instruments produce overtones.
The natural frequency is set by the properties of the system. The natural frequency of a pendulum is determined by its length (and the strength of gravity). The natural frequency of a spring-mass system is determined by the spring’s stiffness and amount of mass hanging from the spring. The natural frequency of a string is determined by its length, its mass and how tightly the string is stretched.
The easiest way to determine the natural frequency of a system is to give the system a quick shock and watch (or listen) to its response. Give a person on a swing a push and measure the frequency of the resulting motion. Strike a tuning fork (or pluck a guitar string) and find the frequency of the result sound. If the system has a single natural frequency, it will respond by vibrating at that natural frequency. If the system has several natural frequencies, it will respond by vibrating in a complex motion that includes many natural frequencies- almost musical instruments produce overtones because almost all vibrating systems have multiple (but distinct) natural frequencies. Not every system or object has a natural frequency. Give the wall a whack, and it responds with a dull thud. Rub two pieces of sandpaper together and you get noise (i.e. a random mix of wide band of frequencies with no distinct fundamental frequency).
The presence of natural frequencies in a structure can be a blessing or a curse. The presence of natural frequencies in strings allows violinists to reliably produce the pitches they want (and not others). The natural frequencies of the hairs in our inner ear allow us to perceive pitch. The presence of natural frequencies in some objects can can also be disastrous. When exposed to vibrations, such objects can vibrate uncontrollably at their natural frequency- literally shaking themselves to d