An equation that gives the particle displacement for a medium in which there is a simple harmonic traveling wave is , where x and y are in centimeters and t is in seconds. At t = 2 s the speed of a particle at the location x = 4 cm is
A) 0.
B) 2 cm/s.
C) 4 cm/s.
D) 6 cm/s.
E) 8 cm/s.

Question

An equation that gives the particle displacement for a medium in which there is a simple harmonic traveling wave is , where x and y are in centimeters and t is in seconds. At t = 2 s the speed of a particle at the location x = 4 cm is
A) 0.
B) 2 cm/s. 
C) 4 cm/s.
D) 6 cm/s.
E) 8 cm/s.

Quizplus · Accepted Answer

First, take the derivative of the equation with respect to time: 
v(x,t)=-2πfAcos(2πf(t-x/v))
Then, plug in x=4 cm and t=2 s: 
v(4,2)=-2π(150 Hz)(0.15 cm)cos(2π(150 Hz)(2 s-4 cm/150 Hz)/1)=4 cm/s

An Equation That Gives the Particle Displacement for a Medium