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

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Homework Help Overview

The problem involves determining the fundamental frequency of a vibrating string based on two successive overtones, specifically given as 360 Hz and 400 Hz.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between overtones and the fundamental frequency, questioning how to identify the integer multiples associated with the given frequencies.

Discussion Status

Some participants have offered a potential approach by setting up equations based on the definitions of overtones, while others express confusion about identifying the necessary integers. There appears to be a productive exchange of ideas regarding the setup of the problem.

Contextual Notes

Participants are working within the constraints of the problem, focusing on the definitions of overtones and their relationship to the fundamental frequency without additional context or information.

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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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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