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

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

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 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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