4.4.4 - Stationary Waves Flashcards
What is a stationary/standing wave?
A wave formed by the interference of two waves travelling in opposite directions.
What must the two waves be in order for a standing/stationary wave to be produced on a string / in a pipe?
- The two waves that overlap must be travelling in opposite directions.
- The two waves must have the same frequency.
- The two waves must have approximately equal amplitudes.
What happens if two waves travelling in opposite directions are completely out of phase / in anti phase?
This leads to a resultant wave of zero amplitude, because the waves cancel each other out.
When are stationary waves produced on strings?
When progressive waves, travelling in opposite directions, are superposed. (However, it is also possible to produce stationary waves using other longitudinal or transverse waves, such as microwaves).
Describe 6 differences between progressive and stationary waves.
Progressive Wave
- Wave profile moves.
- All particles vibrate with the same amplitude.
- Neighbouring particles vibrate with different phases.
- All particles vibrate.
- Transmits the energy
Stationary Wave
- Wave profile does not move.
- Particles between two adjacent nodes vibrate with different amplitudes.
- Particles between two adjacent nodes vibrate in phase.
- Particles at nodes do not vibrate at all.
- Produced by the superimposition of two waves moving in opposite directions.
- Does not transmit the energy
What are nodes?
Points in a stationary wave at which there is no displacement of the particles at any time. Destructive interference has occurred.
What are antinodes?
Points in a stationary wave at which the displacement of the particles varies by the maximum amount. Constructive interference has occurred.
What is the separation between adjacent nodes/antinodes?
λ / 2
where λ is the wavelength of the progressive wave
What are the stationary wave patterns for a stretched string / air columns in a closed tube?
fundamental (1st harmonic) f0: A N
2nd harmonic 3f0: A N A N
3rd harmonic 5f0: A N A N A N
4th harmonic 7f0: A N A N A N A N
What are the stationary wave patterns for a stretched string / air columns in an open tube?
fundamental (1st harmonic) f0: A N A
2nd harmonic 3f0: A N A N A
3rd harmonic 5f0: A N A N A N A
4th harmonic 7f0: A N A N A N A N A
Describe displacement and air pressure at nodes and antinodes.
- At a node, the air displacement is zero, but the air pressure varies.
- A node for displacement is always an antinode for pressure - the particles experience maximum squeezing toward that point.
- There is little change in the spacing between particles at a displacement antinode.
- But the pressure at displacement antinodes barely changes.
How can the speed of sound be measured in air?
Use a tuning fork and a tube of water.
1) The tube is held by a clamp and is moveable so that its length can be altered. Because of the water in the measuring cylinder, the tube is effectively closed at one end.
2) When a tuning fork of known frequency is struck and held at the open end, the air molecules in the tube will vibrate and a stationary wave will be set up in the tube.
3) By listening carefully, the fundamental frequency can be obtained, when the sound is loudest for at the minimum length. This is achieved when the length of the tube is equal to 1/4 λ.
4) The tube can then be lengthened by loosening the clamp, and the loudness of the sound will reduce initially before increasing again to a second maximum loudness when the length of the tube is equal to 3/4 λ.
5) The difference between these two lengths is equal to half the wavelength of the sound, 1/2 λ, and the speed of sound can be determined by multiplying this value by 2 and then by the frequency of the tuning work in Hz.
What is the fundamental mode of vibration (1st harmonic)?
Where the length of a string is half the wavelength, producing the lowest possible frequency called the first harmonic. It is the lowest frequency, highest wavelength that can be produced on a string.
(Other harmonics are whole number multiples of this frequency).
What 3 things is the frequency of the vibrations of a string governed by?
- Its mass per unit length.
- Its tension (this is adjusted when tuning the instrument).
- The length of the string (which is increased or decreased by the musician’s fingers).
