Physics

1) A wave with frequency 3.1 Hz and amplitude 2.7 cm moves in the positive x-direction with speed 5.6 m/s. Determine the wavelength.

2) The equation of a wave along the x-axis is given as: ξ cm = 3.4 sin (1.13 x - 0.75 t)
in which ξ is the displacement. Units on the right hand side are 1/cm for К and 1/s for ω.
Determine the the traveling speed of the wave.

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  1. 1) A wave with frequency 3.1 Hz and amplitude 2.7 cm moves in the positive x-direction with speed 5.6 m/s. Determine the wavelength.

    Distance = rate * time
    here the time is a period 1/f = 1/3.1
    distance = 5.6 m/s * (1/3.1) s

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  2. 2) The equation of a wave along the x-axis is given as: ξ cm = 3.4 sin (1.13 x - 0.75 t)
    in which ξ is the displacement. Units on the right hand side are 1/cm for К and 1/s for ω.
    Determine the the traveling speed of the wave.

    if x changes by L with no change in t, the argument of the sin increases by 2 pi
    (1.13 x - 0.75 t) +2pi = 1.13 (x+L) -.75 t
    so
    2 pi = 1.13 L
    L = 2 pi/1.13

    if t changes by T with no change in x, the argument of the sine changes by 2pi
    1.13x -.75 (t) = 1.13x -.75(t+T)+ 2 pi
    2 pi = .75 T
    T = 2 pi/.75
    rate = distance/time = (2 pi/1.13) /(2 pi/.75) = .75/1.13

    By the way, you can do this by looking for the constant phase speed
    express the argument of the sine as
    (2 pi/L)(x-vt)
    then 2 pi/L x = 1.13 x
    and (2 pi/L)(vt) = .75t
    or
    L = 2 pi/1.13
    v = .75L/2 pi = .75/1.13 again

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