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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?

Respuesta :

Answer:

Percentage change in tension is 3.8%

Explanation:

We have given initially frequency [tex]f_1[/tex] = 440 Hz

Let tension in the string at this frequency is [tex]T_1[/tex]

Now second frequency is [tex]f_2=448.4Hz[/tex]

Frequency in string is given by

[tex]f=\frac{1}{2L}\sqrt{\frac{T}{\mu }}[/tex]

From the relation we can say that

[tex]\frac{f_1}{f_2}=\sqrt{\frac{T_1}{T_2}}[/tex]

[tex]\frac{440}{448.4}=\sqrt{\frac{T_1}{T_2}}[/tex]

[tex]{\frac{T_2}{T_1}}=1.038[/tex]

Percentage change in tension is equal to

[tex]=\frac{T_2-T_1}{T_1}=\frac{T_2}{T_1}-1=(1.038-1)\times 100=3.8[/tex] %

So percentage change in tension is 3.8%

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