# lecture27 - Wa ve M oti on I I Si nusoi dal(har moni c...

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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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Exampl e 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) ? ii) Which particle moves according to y=A sin ( ϖ t) ? iii) If y e (t)=A cos ( ϖ t+ φ e ) for particle e, what is φ e ?
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