Question

I have a device that can generate sounds with frequencies between 800 Hz and 1600 Hz. I also have an unlabeled tuning fork that I need to work out the fundamental frequency of. I find that it resonates at 920 Hz and 1380 Hz, but no other frequencies in that range. What's the lowest frequency that it will resonate at?

Answer 1

Answer:

460 Hz

Explanation:

the given resonating frequency of the device

f₁ =  920 Hz and f₂ =  1380 Hz

fundamental frequency of the device is

f₀ = n₂ - n₁

   = 1380 - 920

   = 460 Hz

expression of frequency of organic pipe open at both ends

$f_0=n\dfrac{\nu}{2l}$

at n = 1

$f_0=\dfrac{\nu}{2l} = 460 Hz$

the frequency ratios of the closed pipe

$f_0:f_1:f_2: ...... =[1:2:3:.........]f_0$

                         =[1:2:3:.........]460 Hz

                         = 460 Hz : 920 Hz : 1380 Hz

so, the lowest frequency for the pipe open at both end is 460 Hz