Live feed: https://youtu.be/9KdF8B384pA
MIT Video with Superposition of Waves:
MIT Video with Doppler Effect:
Stationary sound source produces sound waves at a constant frequency f, and the wave-fronts propagate symmetrically away from the source at a constant speed c. The distance between wave-fronts is the wavelength. All observers will hear the same frequency, which will be equal to the actual frequency of the source where f = f0.
The same sound source is radiating sound waves at a constant frequency in the same medium. However, now the sound source is moving with a speed υs = 0.7 c. Since the source is moving, the center of each new wavefront is now slightly displaced to the right. As a result, the wave-fronts begin to bunch up on the right side (in front of) and spread further apart on the left side (behind) of the source. An observer in front of the source will hear a higher frequency
f = c + 0/c – 0.7c f0 = 3.33 f0 and an observer behind the source will hear a lower frequency
and an observer behind the source will hear a lower frequency
f = c – 0/c + 0.7c f0 = 0.59 f0
Now the source is moving at the speed of sound in the medium (υs = c). The wave fronts in front of the source are now all bunched up at the same point. As a result, an observer in front of the source will detect nothing until the source arrives where f = c + 0/c – c f0 = ∞ and an observer behind the source will hear a lower frequency
f = c – 0/c + c f0 = 0.5 f0
The sound source has now surpassed the speed of sound in the medium, and is traveling at 1.4 c. Since the source is moving faster than the sound waves it creates, it actually leads the advancing wavefront. The sound source will pass by a stationary observer before the observer hears the sound. As a result, an observer in front of the source will detect f = c + 0/c – 1.4c f0 = -2.5 f0 and an observer behind the source will hear a lower frequency
f = c – 0/c + 1.4c f0 = 0.42 f0
A traveling wave moves from one place to another, whereas a standing wave appears to stand still, vibrating in place. In this animation, two waves (with the same amplitude, frequency, and wavelength) are traveling in opposite directions. Using the principle of superposition, the resulting wave amplitude may be written as:
y ( x , t ) = y m sin ( kx – ωt ) + y m sin ( kx + ωt ) = 2 y m sin ( kx ) cos ( ωt )
The animation at above shows two Gaussian wave pulses are traveling in the same medium but in opposite directions. The two waves pass through each other without being disturbed, and the net displacement is the sum of the two individual displacements.