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

460 Hz

Step-by-step 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(\\u)/(2l)`

at n = 1

`f_0=(\\u)/(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