Peoples Physics Concepts

11.6. Sound in a Tube http://www.ck12.org

11.6 Sound in a Tube

• Analyze and solve problems where standing waves are produced in a tube.

Students will learn how to analyze and solve problems where standing waves (and hence sound) is produced in a

tube.

Key Equations

v=λf

for a tube closed at one end

f=nv/ 4 L, wherenis always odd

for a tube open at both ends

f=nv/ 2 L, wherenis an integer

Guidance

In the case of a tube that is open at one end, a node is forced at the closed end (no air molecules can vibrate up

and down) and an antinode occurs at the open end (here, air molecules are free to move). A different spectrum of

standing waves is produced. For instance, the fundamental standing sound wave produced in a tube closed at one

end is shown below. In this case, the amplitude of the standing wave is referring to the magnitude of the air pressure

variations.

This standing wave is the first harmonic and one can see that the wavelength isλ= 4 L. Sincev=λf, the frequency

of oscillation isf=v/ 4 L. In general, the frequency of oscillation isf=nv/ 4 L, wherenis always odd.

Example 1

QuestionThe objects A, B, and C below represent graduated cylinders of length 50 cm which are filled with water

to the depths of 10, 20 and 30 cm, respectively as shown.