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Chapter 17: Q. 16 (page 483)

The fundamental frequency of an open-open tube is 1500 Hz when the tube is filled with 0掳C helium. What is its frequency when filled with 0掳C air?

Short Answer

Expert verified

The frequency of the tube when it is filled with air at $0 掳 C$ is $512 H z$ .

Step by step solution

01

Given information

The fundamental frequency of the open-open tube is $f = 1500 H z$ .

02

Frequency of the tube when it is filled with air

For the open-open tube, the fundamental frequency of the standing wave is $1500 H z$ when the tube is filled with helium gas at $0 掳 C$ .

For the open-open tube, the fundamental frequency of the standing wave is $位 = \frac{2 L}{m}$ .

When the tube is filled with helium gas the fundamental frequency will be

role="math" localid="1650026727240" $f_{h e l i u m} = \frac{v_{h e l i u m}}{位_{1}} = \frac{970 m / s}{2 L} 鈰� (1)$

When the tube is filled with air the fundamental frequency will be

role="math" localid="1650026757106" $f_{a i r} = \frac{v_{a i r}}{位_{1}} = \frac{331 m / s}{2 L} 鈰� (2)$

From (1) and (2)

$\frac{f_{a i r}}{f_{h e l i u m}} = \frac{331}{970} f_{a i r} = \frac{331}{970} 脳 1500 = 512 H z$

Therefore, the frequency of the tube when it is filled with air at $0 掳 C$ is $512 H z$ .

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