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Chapter 11: 11-53P (page 292)

If two successive overtones of a vibrating string are 280 Hz and 350 Hz, what is the frequency of the fundamental?

Short Answer

Expert verified

The fundamental frequency is found as \(70{\rm{ Hz}}\).

Step by step solution

01

The fundamental frequency and the overtones

Since the overtones are integral multiples of the fundamental frequency, the difference among two consecutive overtones gives the fundamental frequency.

02

Given data 

The frequencies of successive overtones are \({f_n} = 280{\rm{ Hz}}\) and \({f_{n + 1}} = 350{\rm{ Hz}}\).

03

Calculation of the fundamental frequency

The fundamental frequency is calculated as;

\({f_1} = {f_{n + 1}} - {f_n}\)

Substitute the given values in the above equation.

\(\begin{aligned}{c}{f_1} &= 350{\rm{ Hz}} - 280{\rm{ Hz}}\\ &= 70{\rm{ Hz}}\end{aligned}\)

Thus, the fundamental frequency is \(70{\rm{ Hz}}\).

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