The document provides the wave function for a harmonic wave traveling in the negative x-direction with a velocity of 2 m/s, period of 1 Hz, and amplitude of 1 m. The wave function is D(x, t)=sin((pi)x+(2pi)t+pi/2), where the phase constant pi/2 is determined using the information that the displacement at t=0 when x=0 is 1 m.

1. Learning Object 1: Harmonic Wave
If a harmonic wave travels in the negative x direction with a velocity of
2.00m/s, a period of 1.00Hz, an amplitude of 1.00m. The displacement of
the harmonic wave at t=0 of a point located at x=0 is 1.00m. Write the
wave function for this harmonic wave.
Solution:
The wave function for negative displacement is D(x,
t)=Asin(kx+wt+O)．
A=amplitude=1.00
k=wave number=w/v=(2pif)/v, which is (2(pi)(1.00))/2.00=pi
w=2pif=2pi(1.00)=2pi
O=phase constant=?
So, D(x, t)=sin((pi)x+(2pi)t+O)
To determine the phase constant, we must be use the second information
given. The displacement of the wave at t=0 of a point located at x=0 is
1.00. Thus, we set the equation like this
1.00=sin(O)
Then O must be pi/2.
Finally, the equation for this wave is
D(x, t)=sin((pi)x+(2pi)t+pi/2)