Two violinists are trying to tune their instruments in an orchestra. one is producing the desired frequency, 440 hz. the other is producing a frequency of 448.4 hz. by what percentage should the out-of-tune musician change the tension in his string to bring his instrument into tune at 440 hz?

a. 4.0%
b. 0.5%
c. 2.0%
d. 1.0%
e. 0.6%

A. 4.0%

Explanation:

The value of the frequency, f, in a string with a tension, T,  is:

For the well calibrated instrument:

For the instrument to be calibrated

We divide these equations in order to find the rapport between the Tensions:

if the rapport between T2 y T1 is 1.04, it means that the tension in the string should be changed in 4%.

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y