Standing Waves

As two waves moving in opposite directions interference the standing wave is formed. For example interference of wave with its reflection

• Does not propagate but remains stationary i.e. no net propagation of energy
• The amplitude is a superposition of its componenets
• Node: no motion. Antinode: maximum motion

Longitudal standing waves are present in flute, pipe, clarinet etc.. in which the air column in the tube resonates at some characteristic frequencies (harmonics) of the external sound. The longest possible wavelength is called first harmonic (fundamental)

Doppler Effect

You know the sound of a car passing by changes. Not only the intensity (loudness), but also the frequency (wavelength).

• As the source comes towards the observer larger frequency (shorter wavelength) is heard by the observer


• As the source moves away from the observer smaller frequency (longer wavelength) is heard by the observer

Try the applet and take a look to separation of the wavefronts (wavelength).
What happens if the source is moving at the spped of sound or even at a supersonic speed?

The effect takes place if the observer moves also. Or both move. As long as they are in relative motion.

Diffraction

Waves go behind the corners, the legendary ripple tank finally works. No way in real world...

Diffraction patterns are due to interference of different waves, in other words the superposition of the waves.

Try that. Pick up 4 points of minimum intensity and another 4 of maximum intensity. What are the path differences of the two waves in different cases?

• The constructive interference (max intensity) takes place when the path difference is a multiple of the wavelengths.
• How about destructive interference?

There are two loudspeakers in the opposite ends of the room sending 440 Hz. Consider you walk on the line joining the loudspeakers. Describe the sound you hear. What is the minimum distance between the points you do not hear anything at all?

Refraction

Pretty many of you have faced with folded or even uncontinous drinking straw in the soda glass.



































Think about soldiers marching in rows from firm ground to muddy ground. They keep on walking in the same rhythm (frequency).

• How do change the length of the step and the speed? Analogue to wave motion!


• Snell law gives the change in the direction.

Try the explanation by Huygen's principle.

Wave characteristics part 2

As the two pulses meet the result (sum pulse) can be understood by superposition principle. The interference is

• constructive, if the pulses are in phase
• destructive, if the pulses are in opposite phase.

At the boundary between the two media, the pulse is both reflected and refracted (some of the pulse energy is absorped in the end).

1. Reflection

• Phase change (to opposite) takes place, if the pulse is reflected from fixed end
• No phase change, if the pulse is reflected from free end.

2. Refraction

• Take a look to speed, wavelength, phase and amplitude...