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Module 4 - Chapter 12 - Waves 2 II - Coggle Diagram
Module 4 - Chapter 12 - Waves 2 II
Stationary waves
Formation
Forms when two progressive waves with the same frenquecy travelling in opposite directions are superposed
At certain points, they are always in antiphase. This forms a node
Node - points where displacement is always 0, amplidude and intensity are also 0
At certain points, they are always in phase. This forms an antinode
Antinode - point of greatest amplitude and intensity
Properties
Separation between two adjacent nodes/ antinodes equals half the wavelength of the original progressive wave
Frequency is the same as the original wave
Wave profile changes over time
As two progressive waves are travelling in opposite directions, there is no net energy transfer by a stationary wave
Phase difference
In between adjacent nodes, all particles in a stationary wave are oscillating in phase with eachother
All reach maximum positive displacement at same time.
On different side of a node, particles are in antiphase
Particles on one side of a node reach their maximum positive displacement at the same time as those on the other reach their mac negative displacement
, where n is the number of nodes between the points
Comparison
Energy transfer
Progressive - in the direction of the wave
Stationary - no net energy transfer
Wavelength
Progessive - Minimum distance between two adjacent points oscillating in phase
Stationary - twice the distance between adjacent nodes/ antinodes equals the wavelength of the progressive wave that created the stationary wave
Phase difference
Progressive - Phase changes across one complete cycle of the wave
Stationary - All part of the wave between nodes are in phase, and on difference sides of a node are in antiphase
Amplitude
Progressive - all part of the wave have the same amplitude
Stationary - Maximum amplitude occurs at the antinode and drop to zero at the node
Forming
Reflecting microwaves off a metal sheet so two microwaves of the same frequency are travelling in opposite directions
Microwave receiver detects changes in intensity between the nodes/ antinodes
Distance between transmitted and metal sheet needs to be adjusted until the receiver detected a series of nodes/ anodes
Distance between successive notes is
Harmonics
Stationary waves on strings
If a string is strethced between two fixed points, these points act as nodes
When the string is plucked, a progressive wave travels along the string and reflects off its ends
Two progressive waves are created in opposite directions, which form a stationary wave
When the string is plucked it vibrates in its fundamental mode of vibration, where the wavelength of the progressive wave is double the length of the string
Note
Each string has a fundamental mode of vibration
When a wave vibrates a the fundamental frequency, its the first harmonic
Wavelength
Fundamental frequency
is the minimum frequency of a stationary wave for a string
Along with the fundamental mode of vibration, the string can form other stationary waves called harmonics at higher frequencies
For a given string at fixed tension, speed of the progressive waves along the string is constant
If the frequency increases, the wavelength must decrease in proportion
When frequency is ,
, wavelenght is half the wavelength at
Stationary waves in air columns
Stationary waves with sound
Sound wavs reflected off a surface can from a stationary wave
Original wave and reflected wave travel in opposite directions and superpose
Stationary sound waves can be made in tubes by making the air column inside the tube vibrate at frequencies related to the length of the tube
Stationary wave formed depends on whether the ends of the tube are open/ closed
Tube closed at one end
For a stationary wave to form in a closed tube, at the open end there needs to be an anode and at the closed end a node
Air at closed end can't move, so must form a node
At the open end, oscillations of the air are at their greatest amplitude, so it must be an antinode
Frequencies of the harmonics in tubes closed at one end are always an odd multiple of the fundamental frequency
Stationary waves in open tubes
Must have an antinode at each in to form a stationary wave
Harmonics are all integer multiples of the fundamental frequency
Resonance tube
Hold a tuning fork about a tube closed at one end
Air vibratesd at the same frequency as the tuning fork
If the tuning fork is vibrating at the fundamental frequency for the air column, the sound becomes loud, air inside rube resonates
Length of the tube can be changes by raising/lowering it
When the freuqncy of the fork matches
, legth of the tube above water must equal
V = 4L
