Standing Waves in Air Standing Waves in Air ColumnsColumns

Examples: organs, pipes, trumpet

Depends on the reflective end Is it open or closed

Standing Waves in Air Standing Waves in Air ColumnsColumns

Pipe open at both ends Fn = n (V/2L)

n = 1,2,3,… Placement of nodes and antinodes

Both Ends OpenBoth Ends Open

Standing Waves in Air Standing Waves in Air ColumnsColumns

Pipe open at only one end

Only odd harmonics are present Fn = n (V/4L)

n = 1,2,3,… Placement of nodes and antinodes

Closed at One EndClosed at One End

Standing Waves in Air Standing Waves in Air ColumnsColumns

The shape of the instrument can effect the harmonic series

Wind InstrumentsWind Instruments

Wind instruments are not as simple as organ pipes. The shape is not always cylindrical. The holes change the wave patterns as well. The size of the “pipe” varies along the length.

Standing Waves in an Standing Waves in an Air ColumnAir Column

Wind instruments also use standing waves. Flutes, trumpets, pipe organs, trombones, etc.

Some instruments have pipes open at both ends while others have one end closed. Air is free to move at open ends so antinodes

occur. Closed ends are nodes.

The velocity of the wave is now the velocity of sound in air (346 m/s at 25°C).

Problem #1Problem #1

What is the fundamental frequency of a 0.20m long organ pipe that is closed at one end, when the speed of sound in the pipe is 352 m/s?

Problem #2Problem #2

A flute is essentially a pipe open at both ends. The length of a flute is approximately 66.0 cm. What are the first three harmonics of a flute when all keys are closed, making the vibrating air column approximately equal to the length of the flute? The speed of sound in the flute is 340 m/s.

Problem #3Problem #3

What is the fundamental frequency of a guitar string when the speed of waves on the string is 115 m/s and the effective string lengths are as follows: a. 70.0 cm B. 50.0 cm C. 40.0 cm

Problem #4Problem #4

A violin string that is 50.0 cm long has a fundamental frequency of 440 Hz. What is the speed of the waves on this string?