You have a stopped pipe of adjustable length close to a taut 85.0cm, 7.25g wire under a tension of 4170N. You want to adjust the length of the pipe so that, when it produces sound at its fundamental frequency , this sound causes the wire to vibrate in its second overtone (third harmonic). With a very large amplitude. How long should the pipe be?

The length is

Explanation:

From the question we are told that

               The length of the wire  

                The mass is  

                The tension is  

Generally the frequency of  oscillation of a stretched wire is mathematically represented as

Where n is the the number of nodes = 3 (i.e the third harmonic)

              is the linear mass density of the wire

 This linear mass density is mathematically represented as

Substituting values

 Substituting values in to the equation for frequency

From the question the we can deduce that the fundamental frequency is equal to the oscillation of a stretched wire

The fundamental frequency is mathematically represented as

Where is the  length of the pipe

          v is the speed of sound with a value of

    Making   the subject of the formula

   Substituting values

From the question the we can deduce that the fundamental frequency is equal to the oscillation of a stretched wire