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# lecture27 - Wave Motion II Sinusoidal(harmonic)waves x...

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Wave Motion II Wave Motion II Sinusoidal (harmonic) waves Energy and power in sinusoidal waves

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For a wave traveling in the  +x direction, the displacement  y is given by   y (x,t) = A sin ( kx – ϖ t ) with  ϖ = kv A -A y x Remember: the particles in the medium move vertically.
y = A sin ( kx – ϖ t ) = A sin [ constant – ϖ t ]     ω = 2π f ω =“angular frequency” radians/sec f =“frequency”   cycles/sec    (Hz=hertz) The transverse displacement of a particle at a  fixed location  x  in the medium  is a sinusoidal function of time – i.e.,  simple harmonic motion:   The “ angular frequency”  of the particle motion is   ϖ ; the  initial  phase  is  kx  ( different  for different x, that is,  particles).

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Example A -A y x Shown is a picture of a travelling wave,    y=A sin (kx - ϖ t), at the instant for time t=0 . a b c d e i)  Which particle moves according to  y=A cos ( ϖ t)  ?
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