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There is no generic "vibration" equation, as many different things can vibrate with many different boundary conditions. There is, however, a generic wave equation which, as I just hinted at, can be used to formulate equations for specific vibrations.
Given a function u(x,y,z,t) where x, y, and z are spatial coordinates in Euclidean space and t is time, the wave equation is given as:
∂2u/∂t2 = vp2∇2u,
where vp is the phase velocity of the wave and ∇2 is the Laplacian.
For the specific example of a vibrating string with a small amplitude, the wave equation becomes:
∂2y/∂t2 = v2∂2y/∂x2,
where y(x,t) and v is the velocity of the wave.
The remarkable thing about the wave equation is how often Mother Nature uses it. The "u(x,y,z,t)" can describe the vibration of a drum head, the electromagnetic fields of light, the ripples on water, the sound of your voice and much more.
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Is algebra used in music if so how and where?
Yes. The different notes represent different frequencies of vibration. One octave is a vibration ratio of 1 : 2. Since each octave has 12 half-notes, and the vibration ratio is the same for each, the vibration ratio from one half-note to the next is 1 : 12th. root of 2, or 1 : 121/12.Yes. The different notes represent different frequencies of vibration. One octave is a vibration ratio of 1 : 2. Since each octave has 12 half-notes, and the vibration ratio is the same for each, the vibration ratio from one half-note to the next is 1 : 12th. root of 2, or 1 : 121/12.Yes. The different notes represent different frequencies of vibration. One octave is a vibration ratio of 1 : 2. Since each octave has 12 half-notes, and the vibration ratio is the same for each, the vibration ratio from one half-note to the next is 1 : 12th. root of 2, or 1 : 121/12.Yes. The different notes represent different frequencies of vibration. One octave is a vibration ratio of 1 : 2. Since each octave has 12 half-notes, and the vibration ratio is the same for each, the vibration ratio from one half-note to the next is 1 : 12th. root of 2, or 1 : 121/12.
Is the word vibration in the Holy Bible?
In the King James version the word - vibration - does not appear at all. No word beginning with "vib~' appears.
What unit measures vibration?
Vibration has amplitude and frequency, usually defined by acceleration and cycles per second (Hertz). It is measured with an accelerometer.
What is one vibration per second?
What is hertz
What is a equation that is the inverse of the exponential equation?
Logarithmic equation
