A guitar string 0.65 m long has a tension of 61 N and a mass per unit length of 3.0 g/m. (i) What is the speed of waves on the string when i

Question

A guitar string 0.65 m long has a tension of 61 N and a mass per unit length of 3.0 g/m. (i) What is the speed of waves on the string when it is plucked? (ii) What is the string’s fundamental frequency of vibration when plucked? (iii) At what other frequencies will this string vibrate?

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Acacia 5 months 2021-08-18T14:37:04+00:00 1 Answers 19 views 0

Answers ( )

    0
    2021-08-18T14:38:51+00:00

    Answer:

    i

      v  = 142.595 \ m/s

    ii

      f  = 109.69 \ Hz

    iii1 )

      f_2 =219.4 Hz

    iii2)

       f_3 =329.1 Hz

    iii3)

        f_4 =438.8 Hz

    Explanation:

    From the question we are told that

        The length of the string is  l  = 0.65 \ m

         The tension on the string is  T  =  61 \ N

         The mass per unit length is  m =  3.0 \ g/m =  3.0 *  \frac{1}{1000} =  3 *10^{-3 } \ kg /m

         

    The speed of wave on the string is mathematically represented as

           v  = \sqrt{\frac{T}{m} }

    substituting values

          v  = \sqrt{\frac{61}{3*10^{-3}} }

         v  = 142.595 \ m/s

    generally the  string’s  frequency is mathematically represented as

             f  = \frac{nv}{2l}

    n = 1  given that the frequency we are to find is the fundamental frequency

    So

          substituting values

           f  = \frac{142.595 * 1 }{2 * 0.65}

           f  = 109.69 \ Hz

    The  frequencies at which the string would vibrate include

    1       f_2 = 2 * f

    Here f_2 is  know as the second harmonic and the value is  

          f_2 = 2 * 109.69

          f_2 =219.4 Hz

    2

    f_3 =  3 * f

    Here f_3 is  know as the third harmonic and the value is  

          f_3 = 3 * 109.69

         f_3 =329.1 Hz

    3

         f_3 =  4 * f

    Here f_4 is  know as the fourth harmonic and the value is  

          f_3 = 4 * 109.69

         f_4 =438.8 Hz

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