   Chapter 14, Problem 9CQ

Chapter
Section
Textbook Problem

Each of the following questions is related to standing waves in air columns. Choose the words that make each statement correct. (i) For a pipe open at both ends, the harmonic number is equal to the number of [(a) nodes; (b) antinodes]. (ii) The distance from a node to its adjacent antinode is always equal to a [(c) quarter; (d) half] wavelength. (iii) For a pipe closed at one end, the wavelength of the fundamental harmonic equals [(e) two; (f) four] times the pipe length.

(i)

To determine
For a pipe open at both ends the harmonic number is equal to the number of nodes or anti nodes.

Explanation

Given Info: Standing waves on a pipe open at both ends.

The figure below shows the standing wave on a pipe open at both ends.

From the above figures, for the first harmonic, there is node and two antinodes, the pattern is ANNAN , N represents node and AN  represent antinode

(ii)

To determine
The distance from a node to its adjacent antinode in both end open pipe.

(iii)

To determine
The relation between the wavelength and the pipe length of the fundamental harmonic of a pipe closed at one end.

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