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 Strings 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 strings were in unison?

Solution

Correct option is

800 Hz

 

Let T1 be the tension in each strings when they are in unison. Let T2 be the tension in each string when they are not in unison; then since  such that 

                           

                         

Expanding binomially, we have  Thus 

                         

Also,        

                 

Which gives V1 = 800 Hz.

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