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 2−1/12, or about 0.944. That is, the current length is multiplied by 0.944. The length of an unstopped string is 32 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. L(n) = (b)One of the unstopped strings makes an A note. To what length (in centimeters) must the string be stopped in order to make C♯, which is 4 notes higher? (Round your answer to two decimal places.) cm
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 2−1/12, or about 0.944. That is, the current length is multiplied by 0.944. The length of an unstopped string is 32 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. L(n) = (b)One of the unstopped strings makes an A note. To what length (in centimeters) must the string be stopped in order to make C♯, which is 4 notes higher? (Round your answer to two decimal places.) cm
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter4: Exponential And Logarithmic Functions
Section4.CT: Chapter Test
Problem 11CT
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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 2−1/12, or about 0.944. That is, the current length is multiplied by 0.944. The length of an unstopped string is 32 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.
L(n) =
(b)One of the unstopped strings makes an A note. To what length (in centimeters) must the string be stopped in order to make C♯, which is 4 notes higher? (Round your answer to two decimal places.)
cm
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