What distinguishes standing waves from travelling waves?
How does the form of standing waves depend on the boundary conditions?
How can the application of force result in resonance within a system?
the nature and formation of standing waves in terms of superposition of two identical waves travelling in opposite directions
nodes and antinodes, relative amplitude and phase difference of points along a standing wave
standing waves patterns in strings and pipes
the nature of resonance including natural frequency and amplitude of oscillation based on driving frequency
the effect of damping on the maximum amplitude and resonant frequency of oscillation
the effects of light, critical and heavy damping on the system.
The formation of standing waves from the superposition of more than two waves should not be considered.
Pipes will be referred to as open or closed.
End corrections for open pipes are not required.
Boundary conditions for strings include two fixed boundaries, one fixed and one free boundary, and two free boundaries.
Boundary conditions for air in pipes include two closed ends, one closed and one open end, and two open ends.
Vibration modes of air in pipes will be discussed in terms of displacement nodes and antinodes.
For standing waves in air, pressure nodes and antinodes are not required.
The lowest frequency mode of a standing wave will be referred to as the first harmonic. The terms fundamental and overtone are not to be used in this course.
A determination of the wavelength and the frequency of the nth harmonic given the length of the string or pipe and the speed of the wave is required.
Only a qualitative analysis is required concerning the impact of damping on the frequency response of a driven oscillator.
Knowledge of the useful and destructive effects of resonance is required.
Determine the relationship between wavelength and the length for the nth harmonic, and recognize that the harmonic names are set by these relationships, hence the standing waves formed in a pipe with one open and one closed end start with the 1st, 3rd and 5th harmonics.
Workbook;
Standing Waves and Resonance — Student Workbook
Files to support your learning:
Resource - Standing wave questions
Resource - Standing wave practical signal generator
Resource - Standing wave practical resonance tube speed of sound
Resource - Standing wave practical with speaker