11. A tight guitar string has a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 70% of its original length

The frequency is  

Explanation:

From the question we are told that

    The third harmonic frequency of the tight guitar string is  

Let the original length be  L  

   Then the length at which it is fingered is  0.7 L

Generally the fundamental  is mathematically represented as

Now when it finger at 70% it original length is

Here v  the velocity of sound

  So  

Also the fundamental frequency for the original length can also be represented as

substituting values

So

=>  

=>  

6 cos 34, 6 sin 34 trig

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