A wave of amplitude .30 m interferes with a second wave of amplitude .20 m. What are the largest and smallest displeacements that can occur? What type of interference is demonstrated by each displacement?

The largest displacement possible is 0.3 + 0.2 = 0.5 (which corresponds to constructive interference). The lowest is 0.3 - 0.2 = 0.1 (which corresponds to destructive interference).

Well, let me do some math acrobatics for you! When two waves interfere, we need to consider the principle of superposition.

The largest displacement occurs when the waves are in phase and add up constructively. So, the largest displacement would be 0.30 m + 0.20 m, which gives us a whopping 0.50 m. That's like a wave stretching its muscles after a heavy workout!

On the flip side, the smallest displacement happens when the waves are out of phase and cancel each other out destructively. In this case, the smallest displacement would be the difference between the two amplitudes: 0.30 m - 0.20 m = 0.10 m. It's like a wave having a bad hair day and just trying to disappear into the background.

Now, as for the type of interference, when the waves add up constructively, it's called constructive interference. It's like they're giving each other high-fives and saying, "You go, wave!" On the other hand, when they cancel each other out destructively, it's called destructive interference. It's like they're playing hide-and-seek and one wave is like, "Hey, can't catch me!"

So, there you have it – the largest displacement is 0.50 m showing constructive interference, and the smallest displacement is 0.10 m showing destructive interference. Waves can be quite the performers, don't you think?

To determine the largest and smallest displacements that can occur when two waves interfere, we need to consider the principle of superposition, which states that the total displacement at any point is the sum of the individual displacements of the waves.

In this case, we have two waves with different amplitudes: the first wave has an amplitude of 0.30 m, and the second wave has an amplitude of 0.20 m. Let's denote the first wave as Wave 1 and the second wave as Wave 2.

1. Largest Displacement:
When the two waves are in phase (crest coincides with crest and trough coincides with trough), their maximum displacements will add up. So the largest displacement will be the sum of their amplitudes, which is 0.30 m + 0.20 m = 0.50 m. This is known as constructive interference, as the waves reinforce each other, resulting in a larger displacement.

2. Smallest Displacement:
When the two waves are out of phase (crest coincides with trough and vice versa), their maximum displacements will cancel each other out. So the smallest displacement will be the difference of their amplitudes, which is 0.30 m - 0.20 m = 0.10 m. This is known as destructive interference, as the waves partially or completely cancel each other, resulting in a smaller displacement.

In summary:
- Largest Displacement: 0.50 m (constructive interference)
- Smallest Displacement: 0.10 m (destructive interference)

To determine the largest and smallest displacements that can occur when the two waves interfere, we need to consider the type of interference they demonstrate. There are two types of interference: constructive interference and destructive interference.

Constructive interference occurs when the crests of one wave align with the crests of the other wave, resulting in an increase in amplitude. In this case, the displacements add up, creating a larger overall amplitude.

Destructive interference occurs when the crests of one wave align with the troughs of the other wave, resulting in a decrease in amplitude. In this case, the displacements cancel each other out, leading to a smaller overall amplitude.

Given that the amplitude of the first wave is 0.30 m and the amplitude of the second wave is 0.20 m, let's consider both scenarios:

1. Constructive Interference:
The largest displacement occurs when the two waves add up. In this case, the maximum total displacement is the sum of the individual displacements:
Largest Displacement = Amplitude of Wave 1 + Amplitude of Wave 2
Largest Displacement = 0.30 m + 0.20 m = 0.50 m
Therefore, the largest displacement that can occur is 0.50 m, and it demonstrates constructive interference.

2. Destructive Interference:
The smallest displacement occurs when the two waves cancel each other out. In this case, the minimum total displacement is the difference between the amplitudes of the two waves:
Smallest Displacement = Amplitude of Wave 1 - Amplitude of Wave 2
Smallest Displacement = 0.30 m - 0.20 m = 0.10 m
Therefore, the smallest displacement that can occur is 0.10 m, and it demonstrates destructive interference.

To summarize:
- The largest displacement is 0.50 m, and it demonstrates constructive interference.
- The smallest displacement is 0.10 m, and it demonstrates destructive interference.