Question

There is a string of uniform length.In the first case,it vibrates in 1 loop.In 2nd case,it vibrates in 2 loops.In 3rd case,it vibrates in 3 loops.find the ratio of the frequencies between 1st and 3rd case.Also find the ratio of wavelengths between 1st and 3rd case.Show the calcultions.

Answer 1

let their vibrations be x,
 ∴ In first case vibration = 1x
     in 2nd case vibration= 2x
    in the 3rd case vibartion= 3x

ie., their freq = 1x : 2x : 3x.
         
                  ratio = 1:2:3 Ans.

  wavelenght =1/f
      frequency of first case = 1 / x
      frequency of 2nd case = 1/ 3x

i.e, ratio of their frequency = 1/x:1/3x
                                          = 3:1 Ans.