Book edition 1st Edition

Author(s) Paul Peter Urone

Pages 1272 pages

ISBN 9781938168000

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Short Answer

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.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

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,

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

The fundamental frequency is f₁ = 32 Hz

The second harmonic is,

$f_{3} = 3 \times \frac{v}{2 I} = 3 \times 32 = 96 H z$

The second harmonic is,

$f_{5} = 5 \times \frac{V}{2 I} = 5 \times 32 = 160 H z$

The third harmonic is,

$f_{7} = 7 \frac{V}{2 I} = 7 \times 32 = 224 H z$

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

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College Physics (Urone)

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Short Answer

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.)

Step by Step Solution

Step 1: Given Data

Step 2: Calculation of the harmonics

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College Physics (Urone)

Answers without the blur.

Short Answer

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.)

Step by Step Solution

Step 1: Given Data

Step 2: Calculation of the harmonics

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