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  1. #1
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    Vibration impact on cables - theoretical analysis

    A conductor moving in a magnetic field will create a voltage proportional to the length of the conductor, the strength of the magnetic field, and the velocity the conductor is moving through the magnetic field.

    emf=l*h*v

    This is Faradayís Law.
    l=length of the conductor in meters
    h=field strength in Teslaís
    v=velocity of the conductor in meters/sec.

    The earthís magnetic field is about 0.00005 Tesla.
    A 1m cable vibrating with a velocity of 1 m/s would create. 50 uV signal which is actually well above the noise floor of a good system.

    Here is the derivation.



    I used a sine wave in the analysis to make the math simple. Arbitrary waveforms can be analyzed using Fourier analysis.

    The amplitude A of a vibration needed to create a velocity v of the same conductor is simply A=v/w where w= angular velocity = 2*Pi*f where f = frequency of the vibration.

    So, at 1 kHz and a velocity of 1 m/sec we get an amplitude of 160 microns. About the width of a human hair. Slightly larger than an RCH, probably about the same width as a muggeseggele. (Look it up)

    Is this audible? I donít know and itís not my purpose here to make that call. Believers will believe, non-believers wonít - pretty cut and dried.

    Suffice it to say that a small amount of movement in a wire is enough to create a voltage that will turn your beautiful 24 bit signal (really only 21 bits but thatís a subject for another day) into a 14 bit one.


    Somebody asked about vibration effects on other electronic components. Sure, there are plenty. Common ceramic capacitors with high Q dielectrics like X7R and COG exhibit piezoelectric properties and so can create voltages under vibration. This is especially true of MLCC SMT capacitors. Other large film and foil capacitors will also exhibit value modulation under vibration. The Crystal oscillators that are so foundational to digital audio are very susceptible to even small vibrations, which modulate their output frequency.
    Tom

    Audio:
    Amati Futura Mains
    Amati Homage VOX Center,
    Proac Response 1sc Rears,
    Three MC2301's for L,C,R
    MC 602 for the rears
    C 1100, MX 151, MCD 1100, MR 77
    Nottingham Dais with Sumiko Palo Santos Presentation
    SurfacePro 3, JRiver, WW Starlight Platinum USB, Schiit Yggdrasil, Benchmark DAC3 HGC

    Video:
    MX 151, OppO BDP-95, JVC RS-500 DILA projector, 106" diagonal Stewart Luxus Screenwall Deluxe with Studiotek 130 G3 material.

    Lake House:
    Ohm F, MC 275V, C2300, MR 80, Rega P3

    OnDeck:
    McIntosh MAC 4300v

  2. #2

    Re: Vibration impact on cables - theoretical analysis

    Quote Originally Posted by W9TR View Post
    A conductor moving in a magnetic field will create a voltage proportional to the length of the conductor, the strength of the magnetic field, and the velocity the conductor is moving through the magnetic field.

    emf=l*h*v

    This is Faradayís Law.
    l=length of the conductor in meters
    h=field strength in Teslaís
    v=velocity of the conductor in meters/sec.

    The earthís magnetic field is about 0.00005 Tesla.
    A 1m cable vibrating with a velocity of 1 m/s would create. 50 uV signal which is actually well above the noise floor of a good system.

    Here is the derivation.



    I used a sine wave in the analysis to make the math simple. Arbitrary waveforms can be analyzed using Fourier analysis.

    The amplitude A of a vibration needed to create a velocity v of the same conductor is simply A=v/w where w= angular velocity = 2*Pi*f where f = frequency of the vibration.

    So, at 1 kHz and a velocity of 1 m/sec we get an amplitude of 160 microns. About the width of a human hair. Slightly larger than an RCH, probably about the same width as a muggeseggele. (Look it up)

    Is this audible? I donít know and itís not my purpose here to make that call. Believers will believe, non-believers wonít - pretty cut and dried.

    Suffice it to say that a small amount of movement in a wire is enough to create a voltage that will turn your beautiful 24 bit signal (really only 21 bits but thatís a subject for another day) into a 14 bit one.


    Somebody asked about vibration effects on other electronic components. Sure, there are plenty. Common ceramic capacitors with high Q dielectrics like X7R and COG exhibit piezoelectric properties and so can create voltages under vibration. This is especially true of MLCC SMT capacitors. Other large film and foil capacitors will also exhibit value modulation under vibration. The Crystal oscillators that are so foundational to digital audio are very susceptible to even small vibrations, which modulate their output frequency.
    Nice analysis, Tom.

    I've got a simple listening test folks can do for themselves.

    1) Order a pair of Shunyata DF-SS cable suspension system cable supports.
    2) Put a set of the DF-SS supports under one speaker cable only.
    3) Listen to a well-mastered recording where the music is fairly equally distributed between both channels, e.g. a symphonic classical recording.
    4) Compare the channel with the DF-SS cable support to the speaker with it's cables lying on the floor.

    I did this late last year by accident and was surprised by the results.

  3. #3
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    Re: Vibration impact on cables - theoretical analysis

    a] What about the circuit impedance in the above equation?
    b] Remember that a cable has two conductors and the signal is differential mode while this induced voltage is common mode.
    c] Some high-tech cell-phones have accelerometers. So you can actually measure how well different isolators and absorbers work.

  4. #4
    Senior Member
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    Palm Coast, FL 'The Hammock'
    Posts
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    Re: Vibration impact on cables - theoretical analysis

    Quote Originally Posted by Speedskater View Post
    a] What about the circuit impedance in the above equation?
    b] Remember that a cable has two conductors and the signal is differential mode while this induced voltage is common mode.
    c] Some high-tech cell-phones have accelerometers. So you can actually measure how well different isolators and absorbers work.
    Besides accelerometers there are also cell phone apps for Seismometer that work really nice and if you just lay your cell phone on your rack and touch it you can see a reading. Also Vibratio‪n‬ 4+
    Diffraction Limited Design LLC.
    PassXa-30.5, W4S STP, Kef 201/2, KEF 140, Vapor Breeze, Lumin, Bryston CD, BHA-1, HD650, HD800s, Dan Clark 1.1, OPPO 203, 105.

  5. #5

    Re: Vibration impact on cables - theoretical analysis

    Quote Originally Posted by CPP View Post
    Besides accelerometers there are also cell phone apps for Seismometer that work really nice and if you just lay your cell phone on your rack and touch it you can see a reading. Also Vibratio‪n‬ 4+
    Diffraction Limited Design LLC.
    Yep, I use Seismometer; it's a nice graphic display of vibration.

    I'll have to check out Vibration 4+.

  6. #6
    Senior Member
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    Re: Vibration impact on cables - theoretical analysis

    Quote Originally Posted by Speedskater View Post
    a] What about the circuit impedance in the above equation?
    b] Remember that a cable has two conductors and the signal is differential mode while this induced voltage is common mode.
    c] Some high-tech cell-phones have accelerometers. So you can actually measure how well different isolators and absorbers work.
    a) impedance of the wire - at audio frequencies very low.
    b) true - balanced cables with electronics that have decent CMRR would eliminate this issue entirely. For unbalanced interconnects current will flow in the shield.
    c) neat. velocity is the integral of acceleration so should be able to find velocity knowing acceleration.
    Tom

    Audio:
    Amati Futura Mains
    Amati Homage VOX Center,
    Proac Response 1sc Rears,
    Three MC2301's for L,C,R
    MC 602 for the rears
    C 1100, MX 151, MCD 1100, MR 77
    Nottingham Dais with Sumiko Palo Santos Presentation
    SurfacePro 3, JRiver, WW Starlight Platinum USB, Schiit Yggdrasil, Benchmark DAC3 HGC

    Video:
    MX 151, OppO BDP-95, JVC RS-500 DILA projector, 106" diagonal Stewart Luxus Screenwall Deluxe with Studiotek 130 G3 material.

    Lake House:
    Ohm F, MC 275V, C2300, MR 80, Rega P3

    OnDeck:
    McIntosh MAC 4300v

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Vibration impact on cables - theoretical analysis

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