Fundamental Frequency and Greatest Amplitude
Date: Summer 2012
I am doing an experiment in which I pass tones of different frequencies through various materials such as foam and glass and measure the amplitude on the other side in order to determine which material is (generally) the most absorptive material i.e. which material performs well over a range of frequencies and also the relationship between frequency and absorption. My results are in the form of a frequency versus amplitude FFT graph. I know that the peaks are the resonant/natural frequencies of the materials through which I am passing tones, but does the fundamental necessarily have to have the greatest amplitude? (Some of my graphs say otherwise). I would greatly appreciate if you could explain to me how I should interpret these graphs in order to make assertions about what is happening to the sound in terms of absorption and resonance. Some additional information: I do not know if this will help, but the initial amplitude of the tones was kept constant.
The fundamental frequency does not have to be the greatest. Which is greatest can depend on the three-dimensional structure of the object. If the object is contained, it can depend on the container. The interface between the material and the air around it can affect the individual amplitudes, as can the air itself. Even preferences and position of the receiver can affect individual amplitudes. Consider a musical instrument. Many have second and third harmonics with amplitudes greater than the fundamental frequency.
Dr. Ken Mellendorf
Illinois Central College
Assuming that by amplitude, you are speaking of a RMS voltage (V) and not power (Vrms * I). It would surprise me, in the experiment you describe, to discover that the fundamental has the greatest amplitude. When a fundamental is passed through a material, the material will begin to vibrate. First is to absorb the fundamental and then the material will translate that into harmonics of the fundamental, the end(and usually desired) result being resonance. Depending on the fundamental frequency, material, shape, length and the number of each, resonance may develop that has greater amplitude than the fundamental. These effects are additive for the amplitude of frequency.
Please note that the total energy, this is different from amplitude of a frequency, sent in will be greater than the total energy out. It may be wise to measure both V and I of the frequency, and monitor the total power in and out.
Keeping it resonant, Peter E. Hughes, P.H. D., Milford, NH
Click here to return to the Physics Archives
Update: November 2011