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,t 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

Answer 1

21/12 is by 2/12 or geometric Solution! length of unstopped string = 32cm Now the second multiplied should be note by 0.944. by Some Third note, should way multiply The second note 0.944 So 9+ serier with first term =32, and common ratis 2 SO L(n) = ar where a = 32 -1/12 2 =) Lind 32 (21/12) (12) Lind 32 2 n- Lin) -32 (0.944) Lini = 32 321 3 CH +7/12) Or32(0.949) 21/12 oro.gon nt oro.g49 3 (G SO L14) 32 32 [ z tanie] or 32 [0.5 do (321_7 3/12 L(4) =32 (82)19 32(0.944)3 or 32 (0.9 4913 26igt om pop so 214)