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What is the relationship between penetration depth and frequency...
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Mad Max
What is the relationship between penetration depth and frequency...
Dear DIndar, For radiofrequency and optical spectrum, the attenuation of the wave follows an exponential decay: I=I0 e^-(alpha)*d being alpha de absorption coefficient and d the penetration depth. The frequency dependence is on the alpha coefficient, and this is different for different types of waves and boundary conditions. You should look for the specific case.
Dear DIndar, For radiofrequency and optical spectrum, the attenuation of the wave follows an exponential decay: I=I0 e^-(alpha)*d being alpha de absorption coefficient and d the penetration depth. The frequency dependence is on the alpha coefficient, and this is different for different types of waves and boundary conditions. You should look for the specific case.
Dear DIndar, For radiofrequency and optical spectrum, the attenuation of the wave follows an exponential decay: I=I0 e^-(alpha)*d being alpha de absorption coefficient and d the penetration depth. The frequency dependence is on the alpha coefficient, and this is different for different types of waves and boundary conditions. You should look for the specific case.
Dear DIndar, For radiofrequency and optical spectrum, the attenuation of the wave follows an exponential decay: I=I0 e^-(alpha)*d being alpha de absorption coefficient and d the penetration depth. The frequency dependence is on the alpha coefficient, and this is different for different types of waves and boundary conditions. You should look for the specific case.
When you increase the power, could it be that your excitation will also include energy in the higher harmonic mulitples, 2*f0, 3*f0, etc of the f0 excitation? If such higher harmonics are generated, these are more highly damped due to the frequency-dependent attenuation. Moreover, higher harmonics can also be generated for high-amplitude waves also due to pure non-linear propagation effects. These will be more attenuated as well.
When you increase the power, could it be that your excitation will also include energy in the higher harmonic mulitples, 2*f0, 3*f0, etc of the f0 excitation? If such higher harmonics are generated, these are more highly damped due to the frequency-dependent attenuation. Moreover, higher harmonics can also be generated for high-amplitude waves also due to pure non-linear propagation effects. These will be more attenuated as well.
Thank you for your guidance. based on Stokes law of sound attenuation in Newtonian fluid, alpha is proportion with square of frequency. Is it true that any material operates like a filter and have maximum absorption coefficient it means in that frequency penetration depth of wave is minimum? And I have another question. what is the role of wave energy in penetration depth? is there any relationship between wave energy, frequence and peneteration depth?
Thank you for your guidance. based on Stokes law of sound attenuation in Newtonian fluid, alpha is proportion with square of frequency. Is it true that any material operates like a filter and have maximum absorption coefficient it means in that frequency penetration depth of wave is minimum? And I have another question. what is the role of wave energy in penetration depth? is there any relationship between wave energy, frequence and peneteration depth?
I'd say typically, the attenuation of waves increases with frequency, hence the penetration depth decreases. For acoustic waves, it is typically assumed that the attenuation coefficient increases between linearly and quadratically with frequency. I cannot think of any counterexample in acoustics. This also applies to thermal waves. It may be different if the properties of the material are strongly frequency-dependent. (E.g. the earth atmosphere is pretty much transparent to electromagnetic waves in the visible spectrum but absorbs lower and higher wavelengths quite effectively.)
I'd say typically, the attenuation of waves increases with frequency, hence the penetration depth decreases. For acoustic waves, it is typically assumed that the attenuation coefficient increases between linearly and quadratically with frequency. I cannot think of any counterexample in acoustics. This also applies to thermal waves. It may be different if the properties of the material are strongly frequency-dependent. (E.g. the earth atmosphere is pretty much transparent to electromagnetic waves in the visible spectrum but absorbs lower and higher wavelengths quite effectively.)
Penetrating capacity of light waves increases as frequency increases; and penetrating capacity of radio waves (or cell phone waves) increases as frequency decreases. This is applicable for all materials. See end of the reference: https://b-ok.cc/book/3630085/dd3a30
Penetrating capacity of light waves increases as frequency increases; and penetrating capacity of radio waves (or cell phone waves) increases as frequency decreases. This is applicable for all materials. See end of the reference: https://b-ok.cc/book/3630085/dd3a30
Dear DIndar,
For radiofrequency and optical spectrum, the attenuation of the wave follows an exponential decay: I=I0 e^-(alpha)*d
being alpha de absorption coefficient and d the penetration depth. The frequency dependence is on the alpha coefficient, and this is different for different types of waves and boundary conditions. You should look for the specific case.
Dear DIndar,
For radiofrequency and optical spectrum, the attenuation of the wave follows an exponential decay: I=I0 e^-(alpha)*d
being alpha de absorption coefficient and d the penetration depth. The frequency dependence is on the alpha coefficient, and this is different for different types of waves and boundary conditions. You should look for the specific case.
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Dear DIndar,
For radiofrequency and optical spectrum, the attenuation of the wave follows an exponential decay: I=I0 e^-(alpha)*d
being alpha de absorption coefficient and d the penetration depth. The frequency dependence is on the alpha coefficient, and this is different for different types of waves and boundary conditions. You should look for the specific case.
Dear DIndar,
For radiofrequency and optical spectrum, the attenuation of the wave follows an exponential decay: I=I0 e^-(alpha)*d
being alpha de absorption coefficient and d the penetration depth. The frequency dependence is on the alpha coefficient, and this is different for different types of waves and boundary conditions. You should look for the specific case.
More
VOTE
When you increase the power, could it be that your excitation will also include energy in the higher harmonic mulitples, 2*f0, 3*f0, etc of the f0 excitation? If such higher harmonics are generated, these are more highly damped due to the frequency-dependent attenuation.
Moreover, higher harmonics can also be generated for high-amplitude waves also due to pure non-linear propagation effects. These will be more attenuated as well.
When you increase the power, could it be that your excitation will also include energy in the higher harmonic mulitples, 2*f0, 3*f0, etc of the f0 excitation? If such higher harmonics are generated, these are more highly damped due to the frequency-dependent attenuation.
Moreover, higher harmonics can also be generated for high-amplitude waves also due to pure non-linear propagation effects. These will be more attenuated as well.
More
VOTE
Thank you for your guidance.
based on Stokes law of sound attenuation in Newtonian fluid, alpha is proportion with square of frequency. Is it true that any material operates like a filter and have maximum absorption coefficient it means in that frequency penetration depth of wave is minimum?
And I have another question. what is the role of wave energy in penetration depth? is there any relationship between wave energy, frequence and peneteration depth?
Thank you for your guidance.
based on Stokes law of sound attenuation in Newtonian fluid, alpha is proportion with square of frequency. Is it true that any material operates like a filter and have maximum absorption coefficient it means in that frequency penetration depth of wave is minimum?
And I have another question. what is the role of wave energy in penetration depth? is there any relationship between wave energy, frequence and peneteration depth?
More
VOTE
I'd say typically, the attenuation of waves increases with frequency, hence the penetration depth decreases. For acoustic waves, it is typically assumed that the attenuation coefficient increases between linearly and quadratically with frequency. I cannot think of any counterexample in acoustics. This also applies to thermal waves. It may be different if the properties of the material are strongly frequency-dependent. (E.g. the earth atmosphere is pretty much transparent to electromagnetic waves in the visible spectrum but absorbs lower and higher wavelengths quite effectively.)
I'd say typically, the attenuation of waves increases with frequency, hence the penetration depth decreases. For acoustic waves, it is typically assumed that the attenuation coefficient increases between linearly and quadratically with frequency. I cannot think of any counterexample in acoustics. This also applies to thermal waves. It may be different if the properties of the material are strongly frequency-dependent. (E.g. the earth atmosphere is pretty much transparent to electromagnetic waves in the visible spectrum but absorbs lower and higher wavelengths quite effectively.)
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@ Shahab
The "generalized relation" can be found as eq. 40 and 41 in this article https://www.researchgate.net/publication/287249513_Connecting_the_grain-shearing_mechanism_of_wave_propagation_in_marine_sediments_to_fractional_calculus
And why you have encountered "apparent" contradictory information is explained in the paragraph after eq. 42. It explains the competition between phase velocity and attenuation affecting penetration depth. Also see fig 3, 4 and 5 there.
Article Connecting the grain-shearing mechanism of wave propagation ...
@ Shahab
The "generalized relation" can be found as eq. 40 and 41 in this article https://www.researchgate.net/publication/287249513_Connecting_the_grain-shearing_mechanism_of_wave_propagation_in_marine_sediments_to_fractional_calculus
And why you have encountered "apparent" contradictory information is explained in the paragraph after eq. 42. It explains the competition between phase velocity and attenuation affecting penetration depth. Also see fig 3, 4 and 5 there.
Article Connecting the grain-shearing mechanism of wave propagation ...
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Penetrating capacity of light waves increases as frequency increases; and penetrating capacity of radio waves (or cell phone waves) increases as frequency decreases. This is applicable for all materials. See end of the reference: https://b-ok.cc/book/3630085/dd3a30
Penetrating capacity of light waves increases as frequency increases; and penetrating capacity of radio waves (or cell phone waves) increases as frequency decreases. This is applicable for all materials. See end of the reference: https://b-ok.cc/book/3630085/dd3a30
More
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