What Is the Fundamental Frequency If Successive Overtones Are 360 Hz and 400 Hz?

In summary, The fundamental frequency of the vibrating string is 40 Hz, as determined by the difference between successive overtones being 40 Hz and the fact that overtones are integer multiples of the fundamental frequency. The integers for 360 Hz and 400 Hz are 9 and 10, respectively. To find the fundamental frequency, one can use the equation nf = 360 Hz and (n+1)f = 400 Hz, which simplifies to f = 40 Hz.
  • #1
PhysicBeginner
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Hi, everyone I'm really baffled by this question here. So I was wondering if anyone could help me.
Question:
If two successive overtones of a vibrating string are 360 Hz and 400 Hz, what is the frequency of the fundamental?
 
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  • #2
Well the overtones are an integer multiple of the fundamental frequency, f, and if they are successive, then one has nf and (n+1)f.

What would the integers be for 360 Hz and 400 Hz?
 
  • #3
Yes that's the part that troubles me. I don't know how to find the integers.
 
  • #4
So can anybody please help me?
 
  • #5
Try nf = 360 Hz, and (n+1)f = 400 Hz,

which leads one to (n+1)f - nf = 400 - 360 Hz => f = 40 Hz.

so 9f = 9 * 40 Hz = 360 Hz, and 10 * 40 Hz = 400 Hz.
 
  • #6
oh now i get it, thanks
 

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The sound frequency problem is caused by the complex interaction between sound waves and the structures of the human ear, particularly the cochlea, which is responsible for detecting different frequencies of sound.

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The sound frequency problem can affect human hearing in various ways, such as causing difficulty in understanding speech, sensitivity to certain frequencies, and hearing loss in certain frequency ranges.

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To mitigate the sound frequency problem, various solutions can be implemented, such as using hearing aids or assistive listening devices, sound therapy techniques, and creating environments with optimal acoustics.

How is the sound frequency problem studied and researched?

The sound frequency problem is studied and researched through various methods, including experiments with human subjects, computer simulations, and advanced imaging techniques to understand the inner workings of the ear and its response to different sound frequencies.

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