functions of 2 variables?

Question

two people standing 10 feet apart are holding opposite ends of a jump rope. The height of the jump rope x feet from the person on left is given by:
h(x,t)=3+3sin ((pi/10)*x) cos(2pi*t)

give a practical interpretation of each of the following quantities:
a) h(5,2)-h(0,2)
b) h(5,2)-h(5,0)

Answer 1

This is the equation of a "standing wave". You also see this behavior in a wave pool. If you stand by a "faucet" that pulses the water in the pool, the motion will be up and down at any point radially from the center of the faucet.

So the first condition describes the position of the wave at time=2. If you had a camera and took a picture at that time, this is what you would see.
The second condition describes the difference in displacement of the rope from the level of the rope-holders between t=2 seconds and t=0 seconds. So if you stood at this point and took a motion picture for at least 2 seconds, this is what your motion picture would look like.