Question

HELP! Please!

Answer 1

Answer:

a. $d(n)=50 \times 2^{\frac{-12}{12} }$

b. The fret should be placed 25 cm far from the bridge.

c. So, the fraction of string at which the fret is placed is $\frac{1}{2}$.

Step-by-step explanation:

We are given,

The function representing the distance of a fret from the bridge by $d(n)=r \times 2^{\frac{-n}{12} }$,

where r = length of the root note string and n = number of notes higher than root note.

Now, Louis want to produce notes on a 50 com string. This gives r = 50.

Thus, $d(n)=50 \times 2^{\frac{-n}{12} }$.

1. It is required to produce notes which are 1 octave ( 12 notes ) higher than the root note. This gives that n = 12.

So, we get, r = 50 and n = 12 which gives us the function as,

a. $d(n)=50 \times 2^{\frac{-12}{12} }$

i.e. $d(n)=50 \times 2^{-1}$

i.e. $d(n)=\frac{50}{2}}$

i.e. $d(n)=25}$

b. Thus, the fret should be placed 25 cm far from the bridge.

Now, as the fret is placed 25 cm far on the string having length 50 cm.

c. So, the fraction of string at which the fret is placed is $\frac{25}{50}$ i.e. $\frac{1}{2}$.