Question

Two violinists are trying to tune their instruments in an orchestra. One is producing the desired frequency of 440.0 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 440.0 hz?

Answer 1

Answer:

Percentage change in tension is 3.8%

Explanation:

We have given initially frequency $f_1$ = 440 Hz

Let tension in the string at this frequency is $T_1$

Now second frequency is $f_2=448.4Hz$

Frequency in string is given by

$f=\frac{1}{2L}\sqrt{\frac{T}{\mu }}$

From the relation we can say that

$\frac{f_1}{f_2}=\sqrt{\frac{T_1}{T_2}}$

$\frac{440}{448.4}=\sqrt{\frac{T_1}{T_2}}$

${\frac{T_2}{T_1}}=1.038$

Percentage change in tension is equal to

$=\frac{T_2-T_1}{T_1}=\frac{T_2}{T_1}-1=(1.038-1)\times 100=3.8$ %

So percentage change in tension is 3.8%