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?

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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

Correct option is

800 Hz

 

Let T1 be the tension in each strings which  such that

                               

                               

Expanding binomially, we have  Thus

                             

Also,             v2 – v1 = 4           or      v2 = v1 + 4. Therefore,

We have

                          

Which gives v1 = 800 Hz.

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