Resonance Column
Simple Explanation
A resonance column (or resonance tube) is a pipe, closed at one end (often by a water level), used to demonstrate and measure resonance in an air column. When a vibrating tuning fork is held above the open end and the air column length is adjusted, the sound becomes noticeably louder at specific lengths β this is resonance.
Why Do We Need It?
The resonance column is a classic experimental method for measuring the speed of sound, by relating a directly measurable air column length to the known frequency of a tuning fork.
Formula
Resonance Length of a Closed Pipe
L = Ξ»/4 (first resonance)
A pipe closed at one end (like a resonance tube with water) first resonates when its air column length equals one-quarter of the sound wavelength.
- L
- β Length of the air column at first resonance, in metres
- Ξ»
- β Wavelength of the sound wave, in metres
When to use it: Use to find the wavelength (and hence the speed) of sound from the air column length at which a closed resonance tube first resonates with a tuning fork of known frequency.
Worked Example
Finding the speed of sound from a resonance column
A tuning fork of frequency 512 Hz produces the first resonance in a closed tube when the air column length is 0.16 m. Find the speed of sound.
Why Does This Work?
At the closed end of the tube, the air cannot move, forming a node; at the open end, the air moves freely, forming an antinode β the shortest air column that fits this node-at-closed-end, antinode-at-open-end pattern is exactly one-quarter of a wavelength, which is why resonance first occurs at L = Ξ»/4.
Real-Life Example
Blowing across a bottle to produce a note
Blowing across the top of a partially filled bottle produces a musical note.
The air column inside the bottle (closed at the bottom by the liquid) resonates at a specific frequency determined by its length β this is the exact same physics as a resonance column, and is why the pitch changes as you pour liquid in or out, changing the air column length.
Practice
A tuning fork of frequency 440 Hz first resonates in a closed tube at an air column length of 0.19 m. Find the speed of sound.
MediumCommon mistake
Assuming the first resonance occurs when L = Ξ»/2 (as with a string) β a CLOSED pipe has a node at the closed end and an antinode at the open end, giving L = Ξ»/4 for the first resonance, not Ξ»/2.
Quick Review
- A resonance column is closed at one end (node) and open at the other (antinode).
- First resonance: L = Ξ»/4.
- v = fΞ» lets you find the speed of sound from the resonance length and known frequency.