Stationary waves in air and with microwaves Cambridge International AS & A Level Physics revision
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In plain words
Blow across the top of a bottle and it hums: the air inside is vibrating as a stationary wave. The same trick works with microwaves bounced off a metal plate. In each case, finding where the nodes are lets you measure the wavelength.
4 things to know
- In an air column, a closed end is a node (the air there can't move) and an open end is an antinode. The simplest mode of a tube closed at one end fits a quarter of a wavelength into the tube: L = λ ÷ 4.
- A tube open at both ends has an antinode at each end, and its simplest mode fits half a wavelength: L = λ ÷ 2.
- Microwaves aimed at a metal plate reflect and superpose with the waves still arriving, giving a stationary wave. A detector moved along the line finds minima (nodes) half a wavelength apart.
- In every case, the distance between neighbouring nodes is half a wavelength.
Worked example
A tube closed at one end resonates in its simplest mode with a tuning fork of frequency 256 Hz when the air column is 0.33 m long. Find the speed of sound.
- Simplest mode of a closed tube: L = λ ÷ 4, so λ = 4 × 0.33 = 1.32 m.
- v = fλ = 256 × 1.32.
- = 338 m/s, about 340 m/s.
Tips and tricks
- A tube closed at one end gives only the odd multiples of its lowest frequency: f, 3f, 5f.
- Take the antinode to be exactly at the open end. End corrections are ignored.
It lands in your notebook with its questions as flashcards.
Stationary waves in air and with microwaves: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
What is found at the closed end of an air column carrying a stationary wave?
The air there cannot move.
What is found at the open end of an air column carrying a stationary wave?
The air is free to move most there.
A tube of length L is closed at one end. What is the wavelength of its simplest mode?
The tube holds a quarter of a wavelength.
A microwave detector is moved between a transmitter and a metal reflector. Neighbouring minima are 1.5 cm apart. What is the wavelength?
Nodes are half a wavelength apart.
A tube closed at one end has a lowest resonant frequency f. Which of these can it also produce?
Only odd multiples fit a node at one end and an antinode at the other.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
3 questions, 6 marks. Write your answers on paper, then check them.
Stationary waves in air and with microwaves
Cambridge International AS & A Level Physics 9702 · 6 marks · papermunch.org
Name ______________________________ Date ______________
A microwave detector finds neighbouring minima 1.4 cm apart in a stationary wave. Find the wavelength and the frequency of the microwaves.[2]
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2.8 cm, and 1.1 × 10¹⁰ Hz. 3.00 × 10⁸ ÷ 0.028.
A tube open at both ends is 0.50 m long. The speed of sound is 340 m/s. Find its lowest resonant frequency.[2]
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340 Hz. The wavelength is 1.0 m.
A tube closed at one end has a lowest resonant frequency of 85 Hz. Find its next two resonant frequencies.[2]
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255 Hz and 425 Hz.
Answers: Stationary waves in air and with microwaves
- 1. 2.8 cm, and 1.1 × 10¹⁰ Hz. 3.00 × 10⁸ ÷ 0.028.
- 2. 340 Hz. The wavelength is 1.0 m.
- 3. 255 Hz and 425 Hz.