Standing Waves in Air Columns

Monday, 11 June 2018

12:58 PM

A longitudinal sound wave travelling in an air column is reflected at the boundaries

Closed end - a high/low pressure pulse is reflected as-is

Open end - a high pressure is reflected as a low pressure, a low pressure is reflected as a high pressure

A closed end must be a displacement node (pressure antinode)

An open end must be a displacement antinode (pressure node)

Thinking

Given a question, we ultimately want to find the wavelength,

We can get the frequency using

Machine generated alternative text:
Air columns>Closed at one end...
• For one closed and one
open end, the fundamental
mode has
Al = 41.
Wavelength 4 L
Frequency
• In general, only the odd
harmonics can be excited:
Natural frequencies
fn=n
First harmonic
Third harmonic
Fifth harmonic

Machine generated alternative text:
• If both ends are open, the
fundamental mode has
Wavelength = 2 L
Frequency
• All harmonics can be
excited:
Natural frequencies
fn=n—
n =1,2,3
Air columns>Open at both ends...
= 21.
First hannonic
Second harmonic
Third harmonic

End Effects

At the end of an open tube, the antinode occurs a small distance beyond the end of the tube.

This extra length is known as the 'end effect', and should be added onto the length of the tube when calculating the natural frequencies