Question

A tall, thin, slightly flexible steel post of length 5.83 m is fixed upright with one end in the ground. The top end of the post is free to move. What is the lowest frequency standing wave that can be formed on the post, if the wave propagation speed in the steel is 2730 m/s?

Suppose that a standing wave on the post gives rise to a sound wave of the same frequency. A person would be able to hear the sound produced by the above standing wave, since the average human being can detect sounds at frequencies between 20.0 Hz and 20.0 kHz. A nearby mouse, however, can only detect frequencies between 1.01 kHz and 90.0 kHz. What is the lowest harmonic on the post that the mouse can hear?

Answer 1

Given

   length of the steel post l= 5.83 m

   speed of wave propagation v = 2730 m/s

  

it can be considered as closed pipe the fundamental frequency of standing wave is f1 = v/4l

   f1 = v/4l = 2730/(4*5.83) = 117.066 Hz

the frequency of 117 hz sound wave can detect by human being ,

and the mouse can detect the lower frequency is

   f2 = 3v/4l = 3*2730/(4*5.83)= 351.2 Hz

   f3 = 5v/4l = 4*2730/(4*5.83)= 585.33 Hz

   f4 = 7v/4l = 5*2730/(4*5.83) = 819.47 Hz

   f5 = 9v/4l = 5*2730/(4*5.83) = 1053.60 Hz

so the mouse can hear the lowest frequncy is 1053 .60 Hz