Frets are a series of ridges placed across the fingerboard o

Frets are a series of ridges placed across the fingerboard of a guitar. They are spaced so that the sound made by pressing a string against one fret has about 1.0595 times the wavelength of the sound made by using the next fret. The general equation is w_n = w_0(1.0595)^n. Describe the arrangement of the frets on a guitar.

Solution

Sound made by pressing a string against one fret has about 1.0595 times the wavelength of the sound made by using the next fret.

The frets are spaced in a logarithmic scale.

w1 = (1.0595)wo

w2 = 1.0595w1 = (1.0594)^2wo

w3 = w2(1.0595) = w1(1.0595)^2 = w0(1.0505)^3

....... and so , on , wn = wo(1.0595)^n

We can see the sound grows to very high values as we move to further and further on frets.

It grows exponentially

It can be expressed in logarithmic form also

ln(wn/wo) = n*ln(1.0595)

ln(wn/wo) = 0.057*n