Option a - Sight and Wave Phenomena - Notes

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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...
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