Chapter 4.1, Problem 1E

Reminder Round all answers to two decimal places unless otherwise indicated.

A Violin String A violin string is stopped so that the resulting string length makes a desired musical note. In order to make the next higher note, the string must be shortened using a factor of $2$ or about $0.944$. That is, the current length is multiplied by $0.944$. The length of an unstopped string is $32\text{centimeters}$.

a. Find a formula for an exponential function that gives the length $L$, in centimeters, of a string that is stopped to make a tone $n$ notes higher than the unstopped string.

b. One of the unstopped strings makes an $\text{A}$ note. To what length must the string be stopped in order to make $C\#$, which is $4$ notes higher?