## Question

Two identical strings of a stringed musical instrument are in unison when stretched with the same tension. When the tension in one string is increased by 1%, the musician hears 4 beats per second. What was the frequency of the note when the string were in unison?

### Solution

800 Hz

Let T_{1} be the tension in each strings which such that

Expanding binomially, we have Thus

Also, v_{2} – v_{1} = 4 or v2 = v_{1} + 4. Therefore,

We have

Which gives v_{1} = 800 Hz.

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