Where are the node and the antinode in the simplest standing wave in a pipe closed at one end?

There is a node at the closed end and an antinode at the open end, with no other node or antinode in between.

Why must there be a node at the closed end of a pipe?

The air is in contact with the solid end and cannot move backwards and forwards there, so its displacement is permanently zero at that point.

Express the wavelength of the simplest standing wave in a pipe of length L closed at one end.

The wavelength is 4L, because the distance from a node to the next antinode is a quarter of a wavelength.

Give an expression for the lowest frequency of a pipe of length L closed at one end, in terms of the speed of sound v.

f = v/4L, where v is the speed of sound in air in m s⁻¹ and L is the length of the air column in metres.

Describe the next possible mode of vibration in a pipe closed at one end after the simplest one.

There is a node at the closed end, an antinode one third of the way along, a further node two thirds of the way along and an antinode at the open end, and the wavelength is 4L/3.

CCEA A-Level Physics 1210

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Superposition, Interference and Diffraction

Standing waves in a pipe closed at one end

3 things to know
Unit AS 2

Overview

Recall questions on why there is a node at the closed end and an antinode at the open end, the wavelength of the simplest mode as four times the length, why only odd multiples of the lowest frequency resonate, worked frequency calculations, the effect of warming the air, and the node and antinode counts in higher modes.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Numbers

A pipe closed at one end is 0.25 m long and the speed of sound is 340 m s⁻¹. Calculate its lowest resonant frequency.

Numbers

A pipe closed at one end is 0.170 m long and the speed of sound is 340 m s⁻¹. Calculate its lowest resonant frequency.

Key term

Why is there an antinode at the open end of a pipe?

Questions from this subtopic

Each one with the model answer underneath.

1
Where are the node and the antinode in the simplest standing wave in a pipe closed at one end?
Model answer
There is a node at the closed end and an antinode at the open end, with no other node or antinode in between.
2
Why must there be a node at the closed end of a pipe?
Model answer
The air is in contact with the solid end and cannot move backwards and forwards there, so its displacement is permanently zero at that point.
3
Why is there an antinode at the open end of a pipe?
Model answer
The air at the open end is free to move in and out of the pipe, so the displacement there can reach its maximum value.
4
Express the wavelength of the simplest standing wave in a pipe of length L closed at one end.
Model answer
The wavelength is 4L, because the distance from a node to the next antinode is a quarter of a wavelength.
5
Give an expression for the lowest frequency of a pipe of length L closed at one end, in terms of the speed of sound v.
Model answer
f = v/4L, where v is the speed of sound in air in m s⁻¹ and L is the length of the air column in metres.
6
Describe the next possible mode of vibration in a pipe closed at one end after the simplest one.
Model answer
There is a node at the closed end, an antinode one third of the way along, a further node two thirds of the way along and an antinode at the open end, and the wavelength is 4L/3.

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