The wave function (x,t)=(0.03m)sin(2.2x-3.5t) is for a harmonic wave on a string. (a) In what direction does this wave travel and what is its speed? (b) Find the wavelength, frequency, and period of this wave. (c) What is the maximum displacement of any point on the string? (d) What is the maximum speed of any point on the string?

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  1. a. the -3.5t indicates it is moving in the +x direction.
    consider some time t+epsilon after time t. Consider the peak of the wave, so (2.2x-3.5t) is 90 degrees. at time t+e, 2.2x-3.5t-3.5e has to be 90 deg, so x has to increase to keep the max.

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  2. it is y(t) not (x,t)
    y is a function of time

    to stay on the same spot on the wave
    2.2 x - 3.5 t
    must be constant
    that will happen if
    x = (3.5/2.2) t
    well, what does that look like ?
    distance = speed * time :)
    so go right at 3.5/2.2 = 1.59 meters/second
    at t = 0 and x = 0, y = 0
    when is the argument changed by 2pi at x = 0 ?
    3.5 t = 2 pi
    t = 2 pi/3.5 = T the period in seconds
    similarly where is the argument changed by 2 pi at t = 0?
    2.2 x = 2 pi
    x = 2 pi/2.2 = Lambda the wavelength in meters
    sin or cos can never be bigger than one so max y = 0.02 meter
    frequency = 1/T in Hz
    max speed = max of dy/dt = 0.03 * 3.5

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