Question

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%

Answer 1

Answer:

A. 4.0%

Explanation:

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

$f=\sqrt{\frac{T}{4mL} }$

For the well calibrated instrument:

$f_{1}=\sqrt{\frac{T_{1}}{4mL} }$

For the instrument to be calibrated

$f_{2}=\sqrt{\frac{T_{2}}{4mL} }$

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

$T_{2}/T_{1}=(f_{2}/f_{1})^{2}=(448.4/440)^2=1.04$

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