Essential idea: When travelling waves meet they can superpose to form standing waves in which energy may not be transferred.
Nature of science:
Common reasoning process: From the time of Pythagoras onwards the connections between the formation of standing waves on strings and in pipes have been modelled mathematically and linked to the observations of the oscillating systems. In the case of sound in air and light, the system can be visualized in order to recognize the underlying processes occurring in the standing waves. (1.6)
Understandings:
The nature of standing waves
Boundary conditions
Nodes and antinodes
Applications and skills:
Describing the nature and formation of standing waves in terms of superposition
Distinguishing between standing and travelling waves
Observing, sketching and interpreting standing wave patterns in strings and pipes
Solving problems involving the frequency of a harmonic, length of the standing wave and the speed of the wave
Guidance:
Students will be expected to consider the formation of standing waves from the superposition of no more than two waves
Boundary conditions for strings are: two fixed boundaries; fixed and free boundary; two free boundaries
Boundary conditions for pipes are: two closed boundaries; closed and open boundary; two open boundaries
For standing waves in air, explanations will not be required in terms of pressure nodes and pressure antinodes
The lowest frequency mode of a standing wave is known as the first harmonic
The terms fundamental and overtone will not be used in examination questions
International-mindedness:
The art of music, which has its scientific basis in these ideas, is universal to all cultures, past and present. Many musical instruments rely heavily on the generation and manipulation of standing waves
Theory of knowledge:
There are close links between standing waves in strings and Schrodinger’s theory for the probability amplitude of electrons in the atom. Application to superstring theory requires standing wave patterns in 11 dimensions. What is the role of reason and imagination in enabling scientists to visualize scenarios that are beyond our physical capabilities?
Utilization:
Students studying music should be encouraged to bring their own experiences of this art form to the physics classroom
Aims:
Aim 3: students are able to both physically observe and qualitatively measure the locations of nodes and antinodes, following the investigative techniques of early scientists and musicians
Aim 6: experiments could include (but are not limited to): observation of standing wave patterns in physical objects (eg slinky springs); prediction of harmonic locations in an air tube in water; determining the frequency of tuning forks; observing or measuring vibrating violin/guitar strings
Aim 8: the international dimension of the application of standing waves is important in music
standing wave
reflection
Harmonic
Open tube / Closed tube
modes
superposition
fixed / free end
Boundary Condition
nodes / anti-nodes
Kognity Textbook Chap 4 - Use you ACS Login
IB Physics Site: Topic 4 - Comprehensive notes
IB Physics Site: Topic 4 - More notes
Topic 4 Flashcards - Vocab Devo.
Flippin' Physics -
How does the boundary condition affect the reflection?
In the PhET simulation below set the wave type to Pulse and reduce the Damping to zero.
Click on the green Pulse button and observe what happens to the pulse on reflection at the fixed end.
Now change the boundary to Loose End (open end) and again click on the Pulse button and observe the reflection of the pulse from the open end. You should observe that from a fixed end the pulse is inverted whereas from an open end the pulse is not inverted.
Describe the effect of Fixed End, Loose End and No End on the reflection of the pulse.
Propose a model for each scenario.
A guitar string for example, is like a string that has a fixed end at both at both ends of the string. When a guitar string is plucked the wave on the string reflects back from the fixed ends and is inverted each time. The waves on the string interfere to produce a standing wave.
In this experiment you will investigate how the tension in the string affects the velocity of the wave on the string.
Set up the apparatus as shown in the diagram.
Apply a tension to the string using the masses
The tension T in the string is equal to the weight of the masses i.e. T = mg.
Adjust the frequency of vibration f using the signal generator until a standing wave is set up.
The example below shows the second harmonic standing wave. In this case the length of the string is equal to the wavelength λ.
In a Google Sheet, create a data table as shown to collect your data. Share this with your partners.
Using the PIVOTInteractives Simulation:
HL Assignment - Advance Analysis of Standing Waves (2022-24)
NO 2021 Activity
String fixed at one end and open at the other -
Set up the apparatus shown below with the metal strip attached to the vibration generator. Adjust the frequency of the signal generator until a standing wave is set up on the metal strip.
Investigate the effect of the length of the strip on the frequency required to set up a standing wave of the same harmonic.
In this experiment you will determine the speed of sound in air by creating standing waves in an air column. The sound in the pipe will be generated using the Audio Function Generator of a LabQuest2 as shown below -or- a tuning fork.
The length of the air column will be changed by moving the plastic pipe in and out of the measuring cylinder filled with water. The water behaves as a closed end for the pipe. The position of the pipe when loud sounds are produced will be used to determine the wavelength of the sound.
Move the pipe up in the water, for example as shown in the gif below, until you find the shortest length of the air column that produces a loud sound (resonance). This is the first harmonic and the water level is at the first node.
Move the pipe further out of the water until you find the next length of the air column that produces a loud sound. This is the second harmonic - the water level is now at the second node.
Determine the length of the air column between these two points. This length represents one half of a wavelength (the distance between two adjacent nodes represents ½ of a wavelength).
REPEAT 2 more times
From the wavelength of the standing wave and the frequency of the sound, calculate the speed of sound in air using c=f𝝀
Repeat for 2 additional frequencies and compare your calculated values of speed of sound with the accepted values.
Standing waves in air columns can be visualised by placing cork powder in the air column and connecting a loudspeaker to one end, as shown below. While these are interesting to observe, they are extremely tedious to setup and observe clear trends. Therefore, it may be easier to observe in video form.
At the position of a node the cork powder does not move.
The diagram below shows the first three harmonics for standing waves in an air column where the pipe is open at both ends and the pipe is closed at one end.
Pressure in standing waves in air columns
In the top simulation below the movement of air particles is shown. The left hand red dot is at a node and its displacement is zero. The right hand red dot is at an antinode and has the maximum displacement.
The middle and bottom graphs show how the longitudinal displacement and pressure vary along the tube. At the point where the displacement of the air particles is zero (i.e. a node) the pressure is an antinode. Notice the changes in density of the particles around each red dot in the top animation. This density of particles is related to the pressure.
While not part of the IB Physics course, the study of instruments are excellent starting points for IA's.
Command terms can be found HERE.