Basic Harmonic Frequencies Question

In summary, the resonant frequencies of a string stretched between fixed supports separated by 82.0 m are 334.000 and 389.667 Hz. The lowest resonant frequency is 334.000 Hz and the wave speed of the string can be calculated by finding the difference between two consecutive resonant frequencies.
  • #1
armolinasf
196
0

Homework Statement



A string is stretched between fixed supports separated by 82.0 m. It is observed to have resonant frequencies of 334.000 and 389.667 Hz, and no other resonant frequencies between these two.

A)What is the lowest resonant frequency of the string?

B)What is the wave speed of this string?


The Attempt at a Solution



I guess I don't really understand this question, Isn't 334 Hz the lowest frequency?
 
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  • #2
Call the fundamental frequency F, then the higher harmonics of the string will have frequencies 2*F, 3*F, 4*F, ...

What you know is m*F = 334.000 Hz, and (m+1)*F = 389.667 Hz

(m+1)*F - m*F = ?
 

1. What are basic harmonic frequencies?

Basic harmonic frequencies refer to the fundamental frequencies of a system or object. These frequencies are the building blocks of more complex waveforms and are typically the lowest frequencies present in a signal.

2. How are basic harmonic frequencies calculated?

Basic harmonic frequencies can be calculated by dividing the fundamental frequency by whole numbers. For example, if the fundamental frequency is 100 Hz, the first harmonic frequency would be 100 Hz, the second harmonic frequency would be 200 Hz, and so on. This is known as the harmonic series.

3. What is the significance of basic harmonic frequencies?

Basic harmonic frequencies are important because they determine the overall pitch and timbre of a sound. They also play a role in the resonance and stability of physical systems.

4. How are basic harmonic frequencies used in music?

In music, basic harmonic frequencies are used to create different notes and chords. By combining different harmonic frequencies, musicians can create complex and pleasing soundscapes.

5. Are basic harmonic frequencies the same for all objects?

No, basic harmonic frequencies can vary depending on the size, shape, and material of an object. For example, a string on a guitar will have different harmonic frequencies than a string on a violin due to their differences in size and material.

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