How to derive Mersenne's fundamental frequency formula?

Thread starter Mars Yeung
Start date Feb 18, 2016
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Derive Formula Frequency Fundamental Fundamental frequency Sound Wave

In summary, Mersenne's fundamental frequency formula is a mathematical equation used to predict the lowest frequency of a vibrating string or column of air. It is derived from principles of physics and mathematics and has been applied in various fields, including music, acoustics, and engineering. However, the formula has limitations in practical applications due to its idealized assumptions. It can be used in real-world situations such as designing instruments, predicting resonant frequencies, and developing technologies like ultrasound and sonar.

Feb 18, 2016

Mars Yeung

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

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Feb 18, 2016

fresh_42

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I don't know your source. Can you specify what is given to derive it from?

1. What is Mersenne's fundamental frequency formula?

Mersenne's fundamental frequency formula is a mathematical formula that predicts the fundamental frequency (also known as the lowest possible frequency) of a vibrating string or column of air. It was discovered by French mathematician and theologian Marin Mersenne in the 17th century.

2. How is Mersenne's fundamental frequency formula derived?

Mersenne's fundamental frequency formula is derived from a combination of principles from physics and mathematics. It takes into account the tension and length of the vibrating medium, as well as the density and elasticity of the material. The formula is derived using the fundamental principles of wave mechanics and harmonic motion.

3. What is the significance of Mersenne's fundamental frequency formula?

Mersenne's fundamental frequency formula is significant because it provides a mathematical basis for understanding the relationship between the physical properties of vibrating mediums and the resulting frequency of the vibration. This formula has been used in various fields, such as music, acoustics, and engineering, to calculate and predict frequencies in different systems.

4. What are the limitations of Mersenne's fundamental frequency formula?

While Mersenne's fundamental frequency formula is a useful tool for predicting frequencies in vibrating systems, it has some limitations. It assumes ideal conditions and does not take into account factors such as damping, non-uniformity of the medium, or non-linear behavior. In practical applications, these factors may affect the accuracy of the formula.

5. How can Mersenne's fundamental frequency formula be applied in real-world situations?

Mersenne's fundamental frequency formula can be applied in various real-world situations, such as designing musical instruments, predicting resonant frequencies in buildings and structures, and understanding the behavior of sound in different mediums. It is also used in the development of technologies such as ultrasound and sonar.