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March 25, 2017

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A sinusoidal wave on a string is described by the equation y = (0.169 m) sin (0.713 x - 41.9 t), where x and y are in meters and t is in seconds. If the linear mass density of the string is 10.1 g/m ...

a) ... the phase of the wave at x = 2.27 cm and t = 0.175 s. ?
b)... the speed of the wave ?
c)... the wavelength.
d) ... the power transmitted by the wave. ?

  • physics - ,

    (a) Do you really mean x = 2.27 cm? Or should that be 2.27 m?
    In either case, compute the value of
    0.713 x - 41.9 t and divide it by 2 pi. Whatever is "left over" after the decimal point will tell you the phase, when compared to 2 pi.
    (c) 0.713 m^-1 = (2 pi)/(wavelength)
    wavelength = 8.81 m
    41.9 s^-1= 2 pi f
    f = 6.67 Hz
    (b) speed = (wavelength)*(frequency)
    = 58.75 m/s
    (d) Wave pwer is proportional to frequency and Amplitude^2.

    See the formula at
    http://hyperphysics.phy-astr.gsu.edu/hbase/waves/powstr.html

  • physics - ,

    a) ... the phase of the wave at x = 2.27 cm and t = 0.175 s. ?
    yes x is 2.27 cm. in meter is 0.0227m !

  • physics - ,

    (d) Wave pwer is proportional to frequency and Amplitude^2.
    f=6.669 Hz u=10.1 g/m
    A=0.169 m
    W=41.9
    I tried with the power transmitted formula power=0.5*u*W^2*A^2*v
    But my solution is wrong :(
    I can not find a) and d) :(

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