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

Percentage change in tension is 3.8%

Step-by-step 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=(1)/(2L)\sqrt{(T)/(\mu )}`

From the relation we can say that

`(f_1)/(f_2)=\sqrt{(T_1)/(T_2)}`

`(440)/(448.4)=\sqrt{(T_1)/(T_2)}`

`{(T_2)/(T_1)}=1.038`

Percentage change in tension is equal to

`=(T_2-T_1)/(T_1)=(T_2)/(T_1)-1=(1.038-1)* 100=3.8` %

So percentage change in tension is 3.8%