Resonance in Air Columns

Closed Air Columns

•Column that is closed at one end and open at the other

Demo•Filling a closed air column

•The water produces a vibration in the air column. As the length of the column shortens, the frequency that resonates increases

Closed Air Column

•The closed end of the column acts as a node. To produce a loud sound, an antinode must formed at the open end

•A vibrating tuning fork is held over the column, it sends a vibration through the column and the closed end reflects the wave back

•Nodes and antinodes are created (just like with standing waves)

•Resonance will be heard loudly when antinodes are created in the column and softly when nodes are created at the end of the column.

Terminology•First resonance – occurs when the first possible antinode is at the open end▫Shortest column to produce first loud sound

•Second resonance – occurs when the second possible antinode is at the open end (second loud sound)

Length of Air Column

•L = n ▫L – length of air column to produce the nth loud sound

▫n – number of wavelengths present for the nth loud sound (determine this from diagram)

▫ - wavelength

Let’s try some calculations

Sample ProblemsA vibrating tuning fork is held over the mouth of a column filled with water. The water level is lowered, and the first loud sound is heard when the air column is 10.0 cm long. Calculate the following:

a.) the wavelength of the sound from the tuning fork

b.) the length of the air column for the second resonance

•a) 40.0cm b) 30.0cm

Open Air Column

•Column is open on both sides

•Antinodes can be created at both ends – produces a loud resonance sound

Sample ProblemAn organ pipe, 3.6m long and open at both ends, produces a musical note at its fundamental frequency.

 a) What is the wavelength of the note produced?

b) What is the frequency of the pipe if the speed of sound in air is 346 m/s?

 a) λ = 7.2 m b) f = 48 Hz