Book edition 4th

Author(s) Randall D. Knight

Pages 1240 pages

ISBN 9780133942651

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Short Answer

A bass clarinet can be modeled as a 120-cm-long open-closed tube. A bass clarinet player starts playing in a 20°C room, but soon the air inside the clarinet warms to where the speed of sound is 352 m/s. Does the fundamental frequency increase or decrease? By how much?

The warmer air temperature increases the fundamental frequency by $1.9 H z$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Given information

The length of the open-closed tube is $L = 120 c m = 1.20 m$

The speed of sound is $v = 352 m / s$ .

The fundamental frequency at v=343 m/s

Assume that the strings of the violin have the same tension and same length and therefore the same fundamental wavelength.

The fundamental frequency at the cool room temperature where the speed of sound is $343 m / s$ .

role="math" localid="1650031107837" $f_{c o o l} = \frac{v}{4 L} = \frac{343}{4 \times 1.2} = 71.46 H z$

Increase in the fundamental frequency

Take the ratio $f_{h o t}$ and $f_{c o o l}$ .

$\frac{f_{h o t}}{f_{c o o l}} = \frac{\frac{v_{h o t}}{4 L}}{\frac{v_{c o o l}}{4 L}} = \frac{352}{343} f_{h o t} = \frac{352}{343} \times 71.46 = 73.3 H z$

Thus, the warmer air temperature increases the fundamental frequency.

role="math" localid="1650031592581" $f_{h o t} - f_{c o o l} = 73.33 - 71.46 \approx 1.9 H z$

Therefore, the warmer air temperature increases the fundamental frequency by $1.9 H z$ .

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Answers without the blur.

Short Answer

A bass clarinet can be modeled as a 120-cm-long open-closed tube. A bass clarinet player starts playing in a 20°C room, but soon the air inside the clarinet warms to where the speed of sound is 352 m/s. Does the fundamental frequency increase or decrease? By how much?

Step by Step Solution

Given information

The fundamental frequency at v=343 m/s

Increase in the fundamental frequency

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Select your language

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Answers without the blur.

Short Answer

A bass clarinet can be modeled as a 120-cm-long open-closed tube. A bass clarinet player starts playing in a 20°C room, but soon the air inside the clarinet warms to where the speed of sound is 352 m/s. Does the fundamental frequency increase or decrease? By how much?

Step by Step Solution

Given information

The fundamental frequency at v=343 m/s

Increase in the fundamental frequency

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