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

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The discussion focuses on determining the fundamental frequency from two successive overtones, 360 Hz and 400 Hz. It explains that overtones are integer multiples of the fundamental frequency, denoted as nf and (n+1)f. By setting up the equations, nf = 360 Hz and (n+1)f = 400 Hz, the difference leads to the fundamental frequency being calculated as 40 Hz. The integers corresponding to the overtones are identified as 9 and 10, confirming the relationship. The explanation clarifies the concept for those confused about finding the integers.
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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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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?
 
Yes that's the part that troubles me. I don't know how to find the integers.
 
So can anybody please help me?
 
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.
 
oh now i get it, thanks
 

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