FIGURE EX16.8 is a picture at t = 0 s of the particles in a medium as a longitudinal wave is passing through. The equilibrium spacing between the particles is 1.0 cm. Draw the snapshot graph D(x, t = 0 s) of this wave at t = 0 s.

Question

Graph showing particles in a medium at t=0s for a longitudinal wave, with 1.0 cm spacing.

Accepted Answer

Welcome back, everyone. We are making observations about a wooden board here and we are told that a sound wave travels through the wooden board. Now, each of these positions here represents a wooden particle that was affected by that sound wave. However, we are told that the equilibrium position between each wood particle is four centimeter. So we are tasked with sketching the wave displacement as a function. Here's how we're going to do this. We are told that the equilibrium distance between each wood particle is four centimeters. So I'm gonna make these tick marks below our number line every four centimeters in order to represent our equilibrium position. Now, what I will do is I will label our displaced wooden particles as row one and I will label our equilibrium wooden particles as row two. Now above it, I'm going to calculate a row one particle minus a row two particle. And you'll see what I mean by that. In just a second, this first particle is positioned at zero and the equilibrium particle according to it is also positioned at zero. So zero minus zero is going to be zero for the next 14 minus four is zero. And for this one, we have that the displaced particle is at 10, but that the equilibrium corresponding particle is at eight. So 10 minus eight is positive two. Now, if we go through this method, for each of the displaced wooden particles, we'll be able to get the displaced value for our wooden particles and come up with our function as a result. So let's keep going through this 16 is going to correspond to 12. So it'll be 16 minus 12 is plus 4, 18 corresponds to our equilibrium position in uh spot 16. So 18 minus 16 is plus 2, 20 minus 20 is 0, 22 minus 24 is negative two. The eighth block here was at the equilibrium position of 28. So 24 minus 28 is negative 4, 30 minus 32 is negative 2, 36 minus 36 is zero and 40 minus 40 is zero. So now tracing this, let's say that this, it represents our zero line starting at this block right here. We are going to start going up, we'll reach that maximum of plus four. We'll start going down and then we'll start reaching back into the negative and then back to the positive. So our desired graph should looks something like this to where it initially goes up and then it initially goes down with points on the end. Let's scroll down and see our answer choices here. And as you can see that perfectly corresponds to our final answer of c Thank you all so much for watching. I hope this video helped. We will see you all in the next one.

FIGURE EX16.8 is a picture at t = 0 s of the particles in a medium as a longitudinal wave is passing through. The equilibrium spacing between the particles is 1.0 cm. Draw the snapshot graph D(x, t = 0 s) of this wave at t = 0 s.

Verified Solution

Key Concepts

Longitudinal Waves

Equilibrium Spacing

Snapshot Graph