# Is there just one fundamental frequency?

I read simple definitions of the terms frequency, and fundamental frequency, which defined them thus,

• Frequency: the number of occurrences of a periodic wave during a second
• Fundamental Frequency: the lowest frequency of a periodic wave.

By replacing frequency in the definition of fundamental frequency with the definition of frequency renders the definition 'the fewest occurrences of a periodic wave during a second'.

It seems to me that that the fewest possible occurrences of something must be one. Is the fundamental frequency one cycle per second?

• You are confusing "occurrence" (as in - is it happening?) with the number of times a periodic signal goes through an entire 2π cycle – Floris Apr 15 '14 at 15:32
• I thought by the number of occurrences they meant [[the number of cycles]]. – Hal Apr 15 '14 at 15:42
• It is unfortunate phrasing and can easily lead to confusion (as it did in your case) - especially since it suggests that the number (and thus the frequency) would always have to be an integer, which is emphatically NOT true. – Floris Apr 15 '14 at 15:45
• @Floris, noted. That helps a lot. – Hal Apr 15 '14 at 16:25
• Remember that the second is a rather random length of time, and reality is not limited by what humans chose. We could have defined frequency as occurrences per hour, and the only difference would have been a constant factor 3600. – MSalters Apr 15 '14 at 23:10

The definition of fundamental frequency should be: the lowest frequency of a periodic wave satisfying some boundary conditions.

For example, in the case of the vibrating string: The lowest frequency is determined by the length of the string (top of the image), the tension in the string, and the mass per unit length.

Of course, if there are no boundary conditions, the lowest frequency would be $\nu=0\mathrm{Hz}$ (not $1\mathrm{Hz}$).

• Hm. Then depending on the properties of the string (or a given boundary condition), a wave could cycle more or less than once per second. In those cases, the fundamental frequency could equal 2 or .45? – Hal Apr 15 '14 at 15:17
• @Hal Yes. For a string the exact formula is $\nu=v/2L$. So it depends on the speed of the wave and the length of the string. – jinawee Apr 15 '14 at 15:19
• Yeah, I thought about 0Hz, but the definition of fundamental frequency that I read presupposed the existence of a wave - "the lowest frequency of a periodic wave". – Hal Apr 15 '14 at 15:20
• What do the v and the L in ν=v/2L denote? – Hal Apr 15 '14 at 15:26
• @Hal $v$ speed of wave, $L$ length of the string. – jinawee Apr 15 '14 at 15:27

No. For one, you can have frequency lower than one. Think of Sun's frequency in the skies, it crosses the sky once per day, not one per second.

On the other hand, it crosses the sky in different place every day during the year, until it gets back to where it was today in one year. So in this regard the fundamental frequency is really once per year.

• I think you misunderstood the question - it was "how many" not "how big" . Yes frequencies can be less than 1 Hz - but by definition, the "fundamental frequency" is exactly one frequency. But the last sentence in the question does show that the person asking the question is quite confused. – Floris Apr 15 '14 at 15:30
• No, he's not asking how many fundamental frequencies are out there. He's philosopher. So, he reads "the fewest occurrences during a second" and thinks that nothing can occur fewer than once. While in fact things can can occur 0.5 times per second, for instance. So, I don't understand the idiots who downgraded my answer. – Aksakal Apr 15 '14 at 15:46
• Well I agree that the question is open to your interpretation - but usually calling people who downvote your answer "idiots" is not a good way to engage in dialog. Fair disclosure: I did not downvote your answer. – Floris Apr 15 '14 at 15:51