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Welcome to our Physics lesson on Speed and Acceleration of Oscillating Particles in a Wave, this is the third lesson of our suite of physics lessons covering the topic of General Equation of Waves, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.
Just like in SHM, we can find the speed of oscillating particles in a wave by taking the first derivative of y-position with respect to the time. Be careful not confuse the oscillating speed of particles (it lies in the y-direction and is not uniform) with the wave speed (which is horizontal and uniform). Thus,
Likewise, we obtain for the vertical acceleration of oscillating particles,
A wave oscillates according the equation
where x and y are in metres and t is in seconds. Calculate:
a) From the general equation of waves
And comparing it with the actual equation
we extract the following values:
and
Thus, giving that
we obtain for the wavelength λ
b) Since
we obtain for the period
c) Now we can use the simplified equation of wave
to find the wave speed. Thus,
d) Since the vertical position y of a point of wave at any instant t is given by the equation
and since in the specific case this equation is
we obtain for x = 3 and t = 2
This result means the given point of the wave is at the equilibrium position at t = 2 s.
e) Vertical speed is the first derivative of vertical position in respect to the time. Thus, we have
Thus, for x = 3 and t = 2 we obtain for the vertical speed vy
You have reached the end of Physics lesson 11.2.3 Speed and Acceleration of Oscillating Particles in a Wave. There are 3 lessons in this physics tutorial covering General Equation of Waves, you can access all the lessons from this tutorial below.
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