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Cousin Throckmorton is playing with the clothesline. One end of the clothesline is attached to a vertical post. Throcky holds the other end loosely in his hand, so that the speed of waves on the clothesline is a relatively slow 0.700 m/s . He finds several frequencies at which he can oscillate his end of the clothesline so that a light clothespin 40.0 cm from the post doesn't move. What are these frequencies?

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okpalawalter8

Answer:

The  frequencies are  [tex]f_n = n (0.875 )[/tex]

Explanation:

From the question we are told that

   The speed of the wave is  [tex]v = 0.700 \ m/s[/tex]

   The  length of vibrating  clothesline is  [tex]L = 40.0 \ cm = 0.4 \ m[/tex]

Generally the fundamental frequency is  mathematically represented as

        [tex]f = \frac{v}{2 L }[/tex]

=>     [tex]f = \frac{ 0.700 }{2 * 0.4 }[/tex]

=>     [tex]f = 0.875 \ Hz[/tex]

Now  this other frequencies of vibration experience by the clotheslines are know as harmonics and they are obtained by integer multiple of  the fundamental frequency

So  

   The  frequencies are mathematically represented as

       [tex]f_n = n * f[/tex]

=>     [tex]f_n = n (0.875 )[/tex]

Where  n  =  1, 2, 3 ....