# What is Fundamental frequency: Definition and 88 Discussions

The fundamental frequency, often referred to simply as the fundamental, is defined as the lowest frequency of a periodic waveform. In music, the fundamental is the musical pitch of a note that is perceived as the lowest partial present. In terms of a superposition of sinusoids, the fundamental frequency is the lowest frequency sinusoidal in the sum of harmonically related frequencies, or the frequency of the difference between adjacent frequencies. In some contexts, the fundamental is usually abbreviated as f0, indicating the lowest frequency counting from zero. In other contexts, it is more common to abbreviate it as f1, the first harmonic. (The second harmonic is then f2 = 2⋅f1, etc. In this context, the zeroth harmonic would be 0 Hz.)
According to Benward's and Saker's Music: In Theory and Practice:
Since the fundamental is the lowest frequency and is also perceived as the loudest, the ear identifies it as the specific pitch of the musical tone [harmonic spectrum].... The individual partials are not heard separately but are blended together by the ear into a single tone.

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1. ### Why is the sinusoidal considered the fundamental frequency?

What property of a sinusoid makes it so special? I understand Fourier analysis, but really you could do Fourier using any periodic function as the building block. Sinusoids really do seem to be fundamental though, if you narrow the pass band of a filter with any random signal you will get a...
2. ### Finding the Fundamental Frequency of a Combination: Boas's Method

This problem came from Problems, Section 3 Chapter 7 in ML Boas, Mathematical Methods in Physical Sciences. Boas suggested to make a computer plot. From my computer plot (I use online graphing calculator) and find that the period of the sum is 2. Instead of using computer, I want to find the...
3. ### Fundamental frequency of a rectangular-cavity whistle

I designed a parametric CAD model of a whistle that can be 3D printed. Basically I designed the internal airspaces, put a skin around it, and printed it. Combine two of these in the same enclosing body, with slightly different frequencies, and you get a warbling sound similar to a pea whistle...
4. ### Standing Wave Fundamental Frequency and Particle Vibration

For a wave A sin ( kx - ωt) and a wave A sin ( kx + ωt) traveling opposite to each other, on evaluating by applying superposition principle , the resultant displacement function is 2A sin ( kx ) cos (ωt) . For different Node Anti-node configurations we calculate natural frequencies of the...
5. ### Resonant Lengths in open air column question

Homework Statement An organ pipe 1.2m long and open at both ends produces a note with the fundamental frequency. If the speed of sound in air is 345 m/s, what is the fundamental frequency? Homework Equations Wave equation (f = v/lambda) The Attempt at a Solution My textbook solves the problem...
6. ### Why do Harmonics Decay Faster than the Fundamental?

When looking at the FFT spectrum of a sonometer, I noticed that the harmonics decayed faster than the fundamental. Why is this?
7. D

### Fundamental Frequency Question

Homework Statement A stretched wire vibrates in its first normal mode at a frequency of 369Hz. What would be the fundamental frequency if the wire were one third as long, its diameter were tripled, and its tension were increased two-fold? Homework Equations f = 1/2L * squareroot(Ft/u) The...
8. ### Finding wavelength and fundamental frequency with string

The length of a string is 1328 cm. It is held fixed at each end. The string vibrates in eight sections; i.e., the string has eight antinodes, and the string vibrates at 97 Hz. Find the wavelength and fundamental frequency. I have no clue, anything helps! Thank you!
9. ### Why are there modes in cantilever beam oscillation equations

I'm doing an experiment measuring the relationship between length of a cantilever beam and period of oscillation when I twang it on one end, but I can't seem to understand the equation. The equation for measuring frequency is given here:https://www.hindawi.com/journals/amse/2013/329530/ but I...
10. ### Determining the Fundamental Frequency Component

Suppose you periodically receive samples of a periodic waveform at fixed instances in time Δt. It is known ahead of time that the periodic waveform will have a fundamental frequency component of 50Hz or 60Hz, but perhaps with some higher order harmonics present. What is the easiest way to go...
11. ### Amplitude and phase spectra from fundamental frequency?

Homework Statement Let \begin{equation*} f(t) = 2 + \cos\left( 3t - \frac{\pi}{6} \right) + \frac{1}{4}\cos\left( \frac{1}{2}t + \frac{\pi}{3} \right) + \sin^2(t) \end{equation*} Determine the period ##T## and fundamental frequency ##\omega_0## of ##f## and draw images of its amplitude and...
12. ### Wave's fundamental frequency

Homework Statement A vibrating tuning fork of frequency 512 Hz is held over a water column with one end closed and the other open. As the water level is allowed to fall, a loud sound (resonance) is heard at specific water levels. Assume you start with the tube full of water, and begin steadily...
13. ### Fundamental frequency of a wire wheel spoke

Homework Statement The spoke of a wire wheel is 9.5 cm long, 3.5 mm in diameter, and under tension of 2100 N. The wire is made of steel of density 7860 kg/m3. When struck with a metal tool at its center, the spoke rings at its fundamental frequency. What is that frequency? Homework Equations...
14. ### Waves: fundamental frequency of taut cable

1. Homework Statement The wire cable supporting the mast of a sailboat has a length of 12 m and a linear mass density of 350 g/m. When pushed sideways at its midpoint with a force of 160 N, the cable deflects by 9.5 cm. What is the frequency of the fundamental mode of vibrations on this...
15. ### Will an infinite impedance cause no phase shift?

Homework Statement imgur link: http://i.imgur.com/0Zc8nQe.png Homework Equations Y-Delta transformations The Attempt at a Solution Since it's a proof, I can't check the answer in the back. What I did: I transformed the three impedances in their delta config to a Y config, and my TI89...
16. ### Fundamental frequency change because of bouyant force

Homework Statement A rope has an end fixed and the other is passing through a pulley and has a body attached to it. The fondamental frequency of the rope is initially ##f_1=400 Hz##. If the body is then put in water the fondamental frequency of the rope becomes ##f_2=345 Hz##. If the linear...
17. ### Formula relating thickness of pipe to fundamental frequency

Homework Statement I understand how to find the resonant frequency of a closed pipe but when the thickness of the walls varies, the resonant frequency varies. Is there a formula that i can use to find the resonant frequency of a closed pipe given the length, temperature, speed of sound and...
18. ### What is a method to find the fundamental frequency of a pipe

Homework Statement How can i find the fundamental frequency of a closed piep (measuring cylinder) experimentally/ physicaly. I have done the maths and found the frequency but i want another way to prove this other than simply playing the calculated frequency back at the measuring cylinder. I...
19. ### Music Mystery: 2(Vsound) for the 2nd Harmonic?

Homework Statement A guitar player is plucking a strong of length 30cm. How fast must the player move towards or away from the stationary observer, in order for the observer to mistake the fundamental frequency for the second harmonic? ANSWER: 2(Vsound) towards the observer Homework...
20. ### How to derive Mersenne's fundamental frequency formula?

I'm talking about equation 22, Does anyone know how to derive this? It's Marin Mersenne's formula for fundamental frequency, but I'm perplexed as to how he derived it. L would be the length, F would be force, and μ would be mass per unit length. f is the frequency Thanks
21. ### Fundamental frequency if string halved and tension * 4

Homework Statement The fundamental frequency of vibration of a particular string is f. What would the fundamental frequency be if the length of the string were to be halved and the tension in it were to be increased by a factor of 4? Answer: 4 f 2. The attempt at a solution We have f = f1...
22. ### Fundamental frequency of oscillation in 2 ropes

Homework Statement Homework EquationsThe Attempt at a Solution if the material are the same in both strings, then the density should be the same. v = sqrt (tension/μ) tension in the first string should be 30 kg x 9.8 m/s^2 = 294 N next, v = λƒ and string#2 needs to have twice the...
23. ### Can a harmonic be louder than the fundamental frequency?

This is not a homework question per se, but rather something I have come across during a homework project. Using Audacity, I recorded a few different instruments playing the same notes (investigating timbre). I noticed that (using a steel string acoustic guitar) the first harmonic at 131 Hz...
24. ### Fundamental note vs fundamental frequency of string

Homework Statement A guitr player changes the frequncy of the note produced by a guitar string by pressing his fingers along the string. The fundamental frequency of the string is 264hz. What are the frquncies of the fundamental note if the player plucked the string at 1/4 of the way from one...
25. ### Fundamental frequency of an object with nonlinear stiffness.

Hi all. It's been a few years since I've posted here, but it's remained a great go-to resource for me. Any time I have dealt with mechanical vibrations, the fundamental frequency was based on a constant stiffness. However, I have never encountered the subject of finding the fundamental...
26. ### Fundamental Frequency of a nano scale oscillator (graphene)

Hi everyone, long time lurker, first time poster. I've just begun a phd which involves nanoribbons (a small strip of a 2D material connected at either end to a larger 'bulk' section of the same 2D material). A question has occurred to me. These nanoribbons look a lot like a piece of string...
27. ### Calculating Fundamental Frequency and Overtone Frequency of a Stretched Wire

Homework Statement a flexible wire is 80 cm long has a mass of 0.40g. It is stretched across stops on a sonometer that are 50 cm apart by a force of 500N. Find the fundamental frequency with which the wire may vibrate. If it vibrates in 2 third overtone, what is it's frequency?Homework...
28. ### What is the fundamental frequency of an aluminum rod?

Homework Statement A longitudinal standing wave can be created in a long, thin aluminum rod by stroking the rod with very dry fingers. This is often done as a physics demonstration, creating a high-pitched, very annoying whine. From a wave perspective, the standing wave is equivalent to a...
29. ### Tension and Fundamental frequency

The fundamental frequency of a uniform wire with an AC current of constant magnitude was found at various different tensions and a graph of (T1/2,l) was plotted (l was the length between the two nodes of the wire when the fundamental frequency was found). How would the data on the graph...
30. ### Estimate the fundamental frequency of resonance sound induced by blowi

Homework Statement Estimate the fundamental frequency of resonance sound induced by blowing on the open end of a half liter bottle Homework Equations f= 1c/4L The Attempt at a Solution i don't know the length of L, what's half liter bottle ..? What does it tell you? 2 x f1?
31. ### Amplitude of harmonics higher than fundamental frequency

Dears, I have an vacuum pump creating the vacuum approximately 10^-8 mbar. The rotor consists blades and it's placed in bearings. One side is ceramic bearing and the other one is maglev type(magnetic). I measure noise and vibrations of the pump. Significant peak of both units is naturally at...
32. ### Finding fundamental frequency with length and successive frequencies

Homework Statement Standing waves on a 1.3 m long string that is fixed at both ends are seen as successive frequencies of 24Hz and 48 Hz. What is the fundamental frequency? Homework Equations fo = nv/4L The Attempt at a Solution Okay, so I don't really know if that is the right...
33. ### Fundamental Frequency of Two Pipe Organs

Homework Statement Two organ pipes, open at one end but closed at the other, are each 1.18 m long. One is now lengthened by 2.50 cm Homework Equations λ = nL/4 fn = nv/4L v = λF The Attempt at a Solution Here's what I tried First I tried finding the fundamental frequency...
34. ### Calculating Fundamental Frequency and Wavelength of a Vibrating String

Homework Statement A 90 cm long steel string with a linear density of 1.1g/m is under 200N tension. It is plucked and vibrates at its fundamental frequency. What is the wavelength of the sound wave that reaches your ear in a 20 degree C room? Homework Equations f = 1/2L * sqrt T/mu v...
35. ### Fundamental frequency of a stretched string

Homework Statement The fundamental frequency of a stretched string is 200Hz. when the length of the string is doubled and Tension of the string made 100times the initial Tension, what is the new fundamental frequency of the string. (1) 50 Hz (2) 100 Hz (3) 200Hz (4) 400 Hz (5) 800 Hz...
36. ### Calculating the fundamental frequency of a travelling wave

No idea what to do here, really tough question, can i get some assistance please? Homework Statement The equation of a traveling transverse wave is y=2.0sin 2π(x/30 - t/0.01) where x and y are in centimetres and t is in seconds. When attached at both ends, a string under a tension...
37. ### Diameter and Fundamental Frequency

Homework Statement Two open tubes both have actual length 1m but their diameters are D=1 cm and D=10 cm. Alowing fro end corrections, what are their fundamental frequencies? Homework Equations the only equation in my book that deals with Diamter is N(Critical...
38. ### Finding Fundamental Frequency

Homework Statement Shown in Picture attachment Question number 6 Homework Equations Not sure..I'm fresh on physics at the moment.. :( The Attempt at a Solution Givens T1 = 250N T2 = 160N L1 = 45cm L2 = 56cm f1 = 450Hz f2 = ? I'm pretty clueless at the moment.. :(
39. ### Confused - Max frequency versus fundamental frequency

Confused! -- Max frequency versus fundamental frequency Hello I understand the following question is very silly, however I am not sure about the answer. Let's consider we are saying there is a signal with a frequency of 4 Hz (for example). In such a statement, does it mean the maximum...
40. ### Fundamental Frequency, Shortening the length of the spring

The fundamental frequency of a spring that is 25 cm long is 441 Hz. In order to produce a fundamental frequency, using the same spring of 525 Hz, the string must be shortened to what length? I'm honestly not even sure how to start this question. Please help :(
41. ### Calculate the fundamental frequency of a steel rod

Homework Statement Calculate the fundamental frequency of a steel rod of length 2.00 m. What is the next possible standing wave frequency of this rod? Where should the rod be clamped to excite a standing wave of this frequency? Homework Equations Fn=nv/2L The Attempt at a Solution since the...
42. ### Calculating Fundamental Frequency of Vibrating String

Homework Statement Determine fundamental frequency of a vibrating string if two successive harmonics of the string are 180hz and 270hz Homework Equations f=1/t t=1/f The Attempt at a Solution I want to say its just f=1/t for both of them but it seems to easy?no?
43. ### Fundamental frequency of a standing wave

Homework Statement A standing wave is established in a string of length 150 cm fixed at both ends. The string vibrates in four segments when driven at 140 Hz. Find the wavelength in meters. Find the fundamental frequency. Homework Equations L = Nλ v = fλ The Attempt at a...
44. ### Is the fundamental frequency of a given swing constant?

As mass is independent of the period for SHM?
45. ### Fundamental Frequency of Vibrating String: From 256Hz to ?Hz

Homework Statement The fundamental frequency of a vibrating stretched string of length 1.0m is 256Hz.When the string is shortened to 0.4m with the same tension,the fundamental frequency now become how many Hz? Homework Equations The Attempt at a Solution
46. ### Fundamental frequency of a pipe half-filled with water

Homework Statement A very tall pipe is partially filled as shown. (A vertical pipe is filled with water about halfway, and .85m of air is in the pipe to the open end. The bottom is closed). |**| ^ |**| | |**| .85m |__| _|_ |__| |__| |__| |__| |__| ^^ My attempt at a drawing, where...
47. ### Fundamental Frequency: Odd Harmonic?

Is the fundamental frequency considered an odd harmonic? Thanks for any clarification
48. ### Fundamental Frequency (String Resonance) - stumped

Fundamental Frequency (String Resonance) - velocity problem! Homework Statement Hey guys, i just started working on Fundamental Frequency but am getting confused! A string that is 6.0m long is vibrating with three loops in it. The frequency of the source is 16.5Hz. A)What is the...
49. ### Vibration1 - Fundamental frequency

How to find the fundamental frequency of the component(let it for engine)? How the orders of that frequency is approximated while FEA?
50. ### How to find fundamental frequency

Homework Statement When a 70kg aluminum (density = 2.7 g/cm3) sculpture is hung from a steel wire, the fundamental frequency for transverse standing waves on the wire is 250.0 Hz. The sculpture (but not the wire) is then completely submerged in water. What is the new fundamental frequency...