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Sinusoidal Waves

Sinusoidal Waves. 20.3 and Longitudinal waves. Longitudinal waves. For longitudinal waves the displacement is parallel to the direction in which the wave is traveling. Thus on a snapshot graph the displacement is ∆ x rather than y. The snapshot graph becomes ∆ x verses x.

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Sinusoidal Waves

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  1. Sinusoidal Waves 20.3 and Longitudinal waves

  2. Longitudinal waves • For longitudinal waves the displacement is parallel to the direction in which the wave is traveling. • Thus on a snapshot graph the displacement is ∆ x rather than y. • The snapshot graph becomes ∆ x verses x. • Figure 20.9- visualizing a longitudinal wave

  3. The Displacement • The traveling wave causes the particles of the medium to be displaced from their equilibrium positions. • D to stands for Displacement. • In a transverse wave D is perpendicular to the transfer of energy. • In a longitudinal wave D is parallel to the transfer of energy. • D is a function of both time and position. • The values of both variables-where and when- must be specified before you can evaluate the displacement of D.

  4. Sinusoidal Waves- Sin Waves • A wave source that oscillates with simple harmonic motion (SHM) radiates a sinusoidal wave. • SHM-When the system is displaced from its equilibrium position, a restoring force which resembles Hooke's law tends to restore the system to equilibrium. • The frequency of the wave is the frequency of the oscillating force.

  5. T is the period or the time interval for one cycle of the motion. • The period is related to the wave frequency f by • T= 1/f • As you move from left to right along the snapshot the disturbance repeats itself over and over.

  6. Wave Terms- hand out • Speed • Crest • Trough • Equilibrium position • Displacement-Amplitude • A and –A? • Wavelength • λ • Period • frequency

  7. The Fundamental Relationship • Important relationship between the wavelength and the period of the wave. • Figure 20.12 • Five snapshot graphs at time increments of one quarter the T. • Each point has undergone one complete oscillation. • During a time interval of one T, each crest of sinusoidal wave travels forward a distance of exactly one λ

  8. V= Distance/ time = λ/T • Remember f=1/T • Then v=λf • Fundamental meaning is that a wave moves forward a distance of one wavelength during a time interval of one period. • Can not be applied to a wave pulse- they do not have wavelength or period.

  9. Because the wave speed is a property of the medium while the wave frequency is a property of the source. • λ= v/f = Property of the medium/ property of the source. • Or the wavelength is a consequence of a wave of frequency f traveling through a medium in which the wave speed is v.

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