Option a - Sight and Wave Phenomena - Notes
OPTION A - SIGHT AND WAVE PHENOMENA
1. Standing (or stationary) waves
Formation of standing waves :
When two identical waves travel along a string in opposite directions (ex : flick a rope attached at the other end), they will superpose and create a standing wave (use animation to visualize what happens).
Nodes, antinodes.
Differences between progressive and standing waves :
Wave profile doesn't progress ;
All points between two nodes are in phase (they all reach their maximum at the same time, and come back to zero at the same time as well. On a progressive wave, all the points in a cycle are all out of phase. Which ones are in phase for a progressive wave ?) ;
Some points have zero amplitudes, some have the maximum amplitude, and the rest of the points have an intermediate amplitude.
Stringed instruments :
How do they work ? Example ? What are the constraints ?
Since the ends can't move, they must become nodes.
What are the possible standing waves that can be produced ?
Fundamental and harmonics for as string of length L.
Application on guitar strings, and how to play higher notes : shorten the string, or play a harmonic by placing a finger on the appropriate node (middle for 2nd harmonic).
Standing waves in pipes closed at an end :
What are the constraints regarding nodes and antinodes ?
Which harmonics can be produced ?
The closed end of a tube is an antinode in the pressure (or a node in the longitudinal displacement). The open end of a tube is approximately a node in the pressure (or an antinode in the longitudinal displacement).
Standing waves in open pipes :
What are the constraints ?
Which harmonics can be produced ?
2. The Doppler effect
Moving source :
Moving observer :
Ex. 17-19
Doppler effect and electromagnetic radiations :
This effect applies to any waves, including EMR. But the velocity of light doesn't change depending on the relative velocity of the observer, so that would make the
1. Standing (or stationary) waves
Formation of standing waves :
When two identical waves travel along a string in opposite directions (ex : flick a rope attached at the other end), they will superpose and create a standing wave (use animation to visualize what happens).
Nodes, antinodes.
Differences between progressive and standing waves :
Wave profile doesn't progress ;
All points between two nodes are in phase (they all reach their maximum at the same time, and come back to zero at the same time as well. On a progressive wave, all the points in a cycle are all out of phase. Which ones are in phase for a progressive wave ?) ;
Some points have zero amplitudes, some have the maximum amplitude, and the rest of the points have an intermediate amplitude.
Stringed instruments :
How do they work ? Example ? What are the constraints ?
Since the ends can't move, they must become nodes.
What are the possible standing waves that can be produced ?
Fundamental and harmonics for as string of length L.
Application on guitar strings, and how to play higher notes : shorten the string, or play a harmonic by placing a finger on the appropriate node (middle for 2nd harmonic).
Standing waves in pipes closed at an end :
What are the constraints regarding nodes and antinodes ?
Which harmonics can be produced ?
The closed end of a tube is an antinode in the pressure (or a node in the longitudinal displacement). The open end of a tube is approximately a node in the pressure (or an antinode in the longitudinal displacement).
Standing waves in open pipes :
What are the constraints ?
Which harmonics can be produced ?
2. The Doppler effect
Moving source :
Moving observer :
Ex. 17-19
Doppler effect and electromagnetic radiations :
This effect applies to any waves, including EMR. But the velocity of light doesn't change depending on the relative velocity of the observer, so that would make the