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Q43PE

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Found in: Page 630

### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

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# If a wind instrument, such as a tuba, has a fundamental frequency of 32.0 Hz, what are its first three overtones? It is closed at one end. (The overtones of a real tuba are more complex than this example, because it is a tapered tube.)

The first three overtones are 96 Hz, 160 Hz, 224 Hz.

See the step by step solution

## Step 1: Given Data

The fundamental frequency is 32 Hz.

## Step 2: Calculation of the harmonics

The resonance frequencies of a tube closed at one end are,

${f}_{n}=n\frac{v}{4I},n=1,3,5,...$

The fundamental frequency is f1 = 32 Hz

The second harmonic is,

${f}_{3}=3×\frac{v}{2I}\phantom{\rule{0ex}{0ex}}=3×32\phantom{\rule{0ex}{0ex}}=96Hz$

The second harmonic is,

${f}_{5}=5×\frac{V}{2I}\phantom{\rule{0ex}{0ex}}=5×32\phantom{\rule{0ex}{0ex}}=160Hz$

The third harmonic is,

${f}_{7}=7\frac{V}{2I}\phantom{\rule{0ex}{0ex}}=7×32\phantom{\rule{0ex}{0ex}}=224Hz$

Hence, the first three overtones are 96 Hz, 160 Hz, 224 Hz.

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