A fundamental frequency is the lowest frequency in a resonating system. It is a vital concept in musical instruments and many aspects of engineering. The harmonics of a given wave, for example, are all based on the fundamental frequency. In order to calculate a fundamental frequency, you need the length of the system or wave as well as a handful of other measurements.
Things You'll Need
- Calculator (optional)
Measure the length of the system. This is one half of the wavelength of the wave it carries. For a tube, measure the length of the tube. For a string, measure the length of the string, etc. Record length in meters. If you must measure with millimeters, centimeters, or another unit, make sure that your velocity uses the same length units. For example, use meters if your velocity is in meters per second.
Divide the velocity of your wave by twice the length of the system. If your tube is closed at one end, divide the velocity by four times the length. The result is the fundamental frequency, in cycles per second, or hertz (Hz). The velocity of a sound wave in air at 20 degrees Celsius is 343 meters per second. For example:
For an open tube of length = 0.5 m
The fundamental frequency of a sound wave in the tube is:
343/(2x0.5) = 343/1 = 343 Hz
Calculate the velocity for a wave on a string by dividing the tension by its mass per unit length. Make sure that the units of mass in your measurement of tension are the same as the units in which you notate the mass itself. For example, if you use newtons as your unit of tension, express your mass in kilograms. Take the square root of this quotient. Divide that result by twice the length. The result is the fundamental frequency. For example:
For a piano string of mass 0.02 kg and length 0.5m,
mass per unit length = 0.02 kg/0.5m = 0.04 kg/m
With a tension of 1500 N,
v^2 = 1500 N / 0.04 kg/m = 37500
v = 193.65 m/s
193.65/(2x0.5) = 193.65/1 = 193.65 Hz
- Photo Credit wave form 51 image by chrisharvey from Fotolia.com
How to Calculate Frequency in Hertz
Hertz measures phenomena like sound waves (hearing, music) and electromagnet waves (radio, light). When waves pass from medium to medium, such as...
How to Calculate Frequency
Sound and light are two examples of energy transmission by periodic pulsations, or waves. The frequency of the pulsations, which is the...
How to Calculate Natural Frequency
The natural frequency, also known as the fundamental frequency, refers to the number of times a given event will happen in a...
How to Figure Harmonics Frequencies
Harmonics are generated whenever oscillation occurs, like when a radio transmitter is activated or a string is struck on a musical instrument....
How to Calculate Sampling Frequency
Sampling frequency, also known as sampling rate, is a measure of the number of samples per second in a sound. A sample...
How to Measure Frequencies
Frequency is a measurement of the speed at which an object can pass from one point to another and back again. It...
How to Calculate Frequency of Waves
Waves are pervasive in many areas of science and engineering. Electrical systems use waves to transmit signals, light and sound travel in...
How to Calculate Oscillation Frequency
The frequency of oscillation is the measure of how often a wave peaks in a given time frame. Lots of phenomena occur...
How to Find Resonant Frequencies
A resonant frequency is the natural vibrating frequency of an object and is usually denoted as a f with a subscript zero...
How to Calculate Number Frequency
The frequency with which a given number occurs in a data set could be easily found simply by counting the number of...