Simple Harmonic Progressive Wave

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SUMMARY

The discussion focuses on the propagation direction of a Simple Harmonic Progressive Wave represented by the equation y=A*sin(ωt-kx+φ). It establishes that if the wave number k is positive, the wave crest travels in the positive x direction, while a negative k indicates propagation in the negative x direction. The analysis emphasizes the relationship between the time term ωt and the distance term -kx, which must balance for a stationary observer on the wave crest. Additionally, it highlights the significance of observing the wave at points of maximum downward slope, relevant for practical applications such as surfing.

PREREQUISITES
  • Understanding of wave mechanics and harmonic motion
  • Familiarity with trigonometric functions and their applications in physics
  • Knowledge of wave parameters: amplitude (A), wave number (k), and frequency (ω)
  • Basic concepts of phase in wave propagation
NEXT STEPS
  • Explore the mathematical derivation of wave equations in different media
  • Study the effects of varying wave parameters on wave behavior
  • Learn about the applications of wave mechanics in real-world scenarios, such as surfing dynamics
  • Investigate the relationship between wave speed, frequency, and wavelength
USEFUL FOR

Students of physics, wave mechanics enthusiasts, and professionals in fields such as engineering and oceanography will benefit from this discussion, particularly those interested in the dynamics of wave propagation and its practical applications.

SDewan
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Given a Simple Harmonic Progressive Wave with the equation y=A*sin(ωt-kx+φ) where A is amplitude, k is wave number, ω is frequency of wave and φ is the initial phase.
How to determine in what direction is the wave propagating?
 
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Consider a wave crest. If you sit on the wave crest then your phase (the value inside the parenthesis above) always remains the same. So as time goes by, the change in the distance term ##-kx## must exactly offset the increase in the time term ##\omega t##.
So the crest must be traveling in the positive x direction, as long as k is positive, and vice versa if k is negative.
A more realistic scenario might be sitting on the point of the wave that has greatest downward slope - half way between crest and trough. That's where a surfer would be!
 
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