   Chapter 14.10, Problem 14.6QQ

Chapter
Section
Textbook Problem

A pipe open at both ends resonates at a fundamental frequency fopen. When one end is covered and the pipe is again made to resonate, the fundamental frequency is fclosed. Which of the following expressions describes how these two resonant frequencies compare? (a) fclosed = fopen (b) f closed = 3 2 f open (c) fclosed = 2 fopen (d) f closed = 1 2 f open (e) none of these

To determine
The expression that compares the resonant frequencies of closed and open pipe.

Explanation

Given Info:

The expression for the fundamental frequency of both end open pipe is,

fopen=v2L

• fopen is the fundamental frequency of both end open pipe,
• v is the speed of the sound in air,
• L is the length of the pipe,

The expression for the fundamental frequency one end covered and other end open pipe is,

fclosed=v4L

• fclosed is the fundamental frequency of one end open and the other end closed pipe,
• v is the speed of the sound in air,
• L is the length of the pipe,

Conclusion:

The expression for the fundamental frequency one end covered and other end open pipe is,

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