As a curious individual, you might be wondering if there is any non-digital (naturally existing) mechanism to compare two or more waves. For instance, suppose you have two input waves, wave one and wave two. You want to compare their wavelengths and output if wave one is of lower or higher wavelength than wave two. Is there a mechanism in existence that can perform this function?
First, to answer this question, we must understand the basics of waves, their properties, and their interactions with other media. Wave theory is a scientific theory explaining how waves behave and propagate. It postulates that a physical phenomenon that exhibits both wave-like and particle-like properties, for example, light and electrons, can be described as a wave.
Resonance filtering
Resonance is a physical phenomenon that occurs when a system oscillates with maximum amplitude or efficiently responds to a periodic driving force at a specific frequency called the resonant frequency or natural frequency. For analogy, imagine a swing; when you push a swing at its natural frequency, it moves higher and higher with minimum effort.
There are all manners of physical systems that have a natural oscillation frequency or resonant frequency, be this mechanical, optical, or whatever. When excited by a multi-frequency signal or a broader spectrum, they will amplify their natural frequency more than any other. So in a way, you can think of them as blocking all other frequencies.
When we apply this idea to our wavelength comparison problem, consider a system with a resonant frequency of 100 Hz that can act as a filter. Any real system also has some amount of attenuation due to friction, which is indicated by the δ parameter. Suppose that our system follows the curve δ=0.2ω0.
Let’s now excite this system with a combination of three frequencies: 50, 100, and 200 Hz. The 50Hz excitation will be amplified to about 133% of the input, the 100 Hz excitation to about 240%, and the 200 Hz to only 33% of the input. As the graph shows, you can use any resonant system with strong dampening to filter out the higher frequencies and adjust the cut frequency with the natural frequency of your system.
Real-world examples
There are numerous real-world examples of resonance filtering that occur in natural and synthetic systems. One of the most familiar examples is in musical instruments, where the natural frequency of the instrument itself determines the frequency of the sound produced. Similarly, radio and TV tuners filter out competing frequencies in the broadcast bands to isolate the frequency desired by the user.
In medical imaging, Magnetic Resonance Imaging (MRI) uses resonance frequency of hydrogen atoms in a magnetic field to create images of the internal structures of the body. Chemists use Mass Spectrometry to identify ions, where the mass of the ions is determined using resonance frequency.
Example of Resonance Filtering in musical instruments
// Guitar string example
// String length = 65cm
// Tension = 40N
// Mass per unit length = 0.006 kg/m
// Density of string = Mass/Volume
Density = 0.006/((π/4) * (0.00065)^2) = ~8.27e-6 kg/m^3
Wave speed(V) = (Tension/Density)^(1/2) = (40/8.27e-6)^(1/2) = ~2315 m/s
Frequency(f) = V/(2L) = 11575 Hz
Conclusion
Resonance filtering is a natural and non-digital mechanism to compare the wavelengths of two or more waves. It uses resonant systems to amplify the natural frequency of a system while damping the higher/free frequencies. Resonance filtering occurs in numerous natural and synthetic systems in industry, research, engineering, and everyday life.
Wavelength comparison is an essential process in numerous fields, including material analysis, medical imaging, acoustic design, and engineering. It is, therefore, imperative to understand the basics of resonance filtering and how it can be manipulated for different applications.
Wavelength Comparison of Two Waves
As a curious individual, you might be wondering if there is any non-digital (naturally existing) mechanism to compare two or more waves. For instance, suppose you have two input waves, wave one and wave two. You want to compare their wavelengths and output if wave one is of lower or higher wavelength than wave two. Is there a mechanism in existence that can perform this function?
First, to answer this question, we must understand the basics of waves, their properties, and their interactions with other media. Wave theory is a scientific theory explaining how waves behave and propagate. It postulates that a physical phenomenon that exhibits both wave-like and particle-like properties, for example, light and electrons, can be described as a wave.
Resonance filtering
Resonance is a physical phenomenon that occurs when a system oscillates with maximum amplitude or efficiently responds to a periodic driving force at a specific frequency called the resonant frequency or natural frequency. For analogy, imagine a swing; when you push a swing at its natural frequency, it moves higher and higher with minimum effort.
There are all manners of physical systems that have a natural oscillation frequency or resonant frequency, be this mechanical, optical, or whatever. When excited by a multi-frequency signal or a broader spectrum, they will amplify their natural frequency more than any other. So in a way, you can think of them as blocking all other frequencies.
When we apply this idea to our wavelength comparison problem, consider a system with a resonant frequency of 100 Hz that can act as a filter. Any real system also has some amount of attenuation due to friction, which is indicated by the δ parameter. Suppose that our system follows the curve δ=0.2ω0.
Let’s now excite this system with a combination of three frequencies: 50, 100, and 200 Hz. The 50Hz excitation will be amplified to about 133% of the input, the 100 Hz excitation to about 240%, and the 200 Hz to only 33% of the input. As the graph shows, you can use any resonant system with strong dampening to filter out the higher frequencies and adjust the cut frequency with the natural frequency of your system.
Real-world examples
There are numerous real-world examples of resonance filtering that occur in natural and synthetic systems. One of the most familiar examples is in musical instruments, where the natural frequency of the instrument itself determines the frequency of the sound produced. Similarly, radio and TV tuners filter out competing frequencies in the broadcast bands to isolate the frequency desired by the user.
In medical imaging, Magnetic Resonance Imaging (MRI) uses resonance frequency of hydrogen atoms in a magnetic field to create images of the internal structures of the body. Chemists use Mass Spectrometry to identify ions, where the mass of the ions is determined using resonance frequency.
Example of Resonance Filtering in musical instruments
Conclusion
Resonance filtering is a natural and non-digital mechanism to compare the wavelengths of two or more waves. It uses resonant systems to amplify the natural frequency of a system while damping the higher/free frequencies. Resonance filtering occurs in numerous natural and synthetic systems in industry, research, engineering, and everyday life.
Wavelength comparison is an essential process in numerous fields, including material analysis, medical imaging, acoustic design, and engineering. It is, therefore, imperative to understand the basics of resonance filtering and how it can be manipulated for different applications.