1 / 8

Harmonic Waves

Harmonic Waves. An harmonically oscillating point is described by a sine wave. y = A cos w t An object can take a sinusoidal shape in space. y = A cos kx. 1 wavelength. 1 period. Sinusoidal Behavior. y. t. y. x. Two Variables.

tlucas
Télécharger la présentation

Harmonic Waves

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Harmonic Waves

  2. An harmonically oscillating point is described by a sine wave. y = A cos wt An object can take a sinusoidal shape in space. y = A cos kx 1 wavelength 1 period Sinusoidal Behavior y t y x

  3. Two Variables • To describe a complete wave requires both x and t. • This harmonic motion is for a harmonic wave.

  4. Wave Speed • The speed is related to the wavenumber • v = l/T • v = (2p/k) / (2p/w) • v = w/k • The wavenumber is related to the speed • k = 2p/l = w/v

  5. While boating on the ocean you see wave crests 14 m apart and 3.6 m deep. It takes 1.5 s for a float to rise from trough to crest. What is the wave speed? The time from trough to crest is half a period: T = 3.0 s. The wavelength is l = 14 m. The speed can be found directly: v = l/T = 4.7 m/s. Seasick

  6. Wave Power • Wave energy is proportional to amplitude squared. • E = ½ mv2 = ½ mL(wA)2 • Power is the time rate of change of energy. • Proportional to the speed • Proportional to the amplitude squared

  7. Intensity • Intensity of a wave is the rate energy is carried across a surface area. • This is true for linear and other waves. • For a spherical wave, the intensity I = P/A = P/4pr2

  8. Rope Snake • A garden hose has 0.44 kg/m. A child pulls it with a tension of 12 N, then shakes it side to side to make waves with 25 cm amplitude at 2.0 cycles per second. • What is the power supplied by the child? • Find the power from the speed and frequency. • Now use the equation for power • P = 11 W

More Related