why to look or search at the why? if you can not hear the result
it is so easy to hear the result.just play. but i'm sure this go above your equations
what is harmony?in an equational way?
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Well this is a bit of a no-brainer, but I thought I would share the wealth. Perhaps someone here doesn't know the mechanics. I admit this is a rather simplistic view, as I fail to completely delve into the 2nd order linear homogenous partial differential wave equation. For a one dimensional system it looks like this:
del^2(si)/del(x)^2 = (1/v^2)*del^2(si)/del(t)2
Where x and t are the independent variables and si represents the disturbance.
One classification of waves are known as the harmonic wave functions. These functions characterize some of the simplest waves, i.e. sine and cosine curves. In General, they look something like the following:
Si(x,t) = Asin(k(x-vt))
The equations mentioned below are rooted in the mathematics and geometry of this particular sine function. Now let's get to the specific question at hand.
Why does tightening a guitar string affect the frequency of the sound that is produced when it is plucked? If you want a higher pitched note should you tighten it or loosened it? Why?
By tightening or loosening a guitar string, you are essentially changing the propagation number,k, which is basically a spring constant. It's purpose is to regulate the units, since we are taking the sine of a number whose units are in length. Therefore, k's dimensions are 1/length. We then get a dimensionless quantity and the bookkeeping is acceptable. Tightening of a guitar string will result in higher k values, while loosening it will result in lower k values.
The following equations will give us some insight into what we should expect.
The propagation number is related to the wavelength by the following equation:
k = (2*pi)/lambda
Where lambda represents the wavelength.
Hence, high values for k result in shorter wavelengths. From here we use the following equation to figure out what happens to the frequency:
nu = v/lambda
Where nu is frequency and v is phase velocity.
In our case, v is taken to be a constant, which happens to be the speed of sound.
It is easy to see that when the wavelength drops off the frequency will increase. Higher frequencies yield higher pitch tones, while lower frequencies generate lower tones.
why to look or search at the why? if you can not hear the result
it is so easy to hear the result.just play. but i'm sure this go above your equations
what is harmony?in an equational way?
why bathe everything in a sea of complex equations???
surely its better just to say that it is because it makes the string vibrate faster?
(that is why isnt it??? i dont understand your equation at all lol)
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