SOLUTION: wave interference worksheet - Studypool - Free Printable

Let's go through each question on the Wave Interference Worksheet and solve them step by step with explanations.

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1. The wavelength of the wave in the diagram below is given by letter ____ and the amplitude of the wave is given by letter ____.

Looking at the wave diagram:

- Wavelength: The distance between two consecutive crests (or troughs). In the diagram, A measures from crest to crest → this is the wavelength.
- Amplitude: The maximum displacement from the equilibrium (rest) position. This is shown as B, which goes from the centerline to the top of a crest.

✔ Answer:
- Wavelength: A
- Amplitude: B

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2. A sine curve that represents a transverse wave is drawn below. Use the centimeter ruler to measure the wavelength and amplitude of the wave (include units)

We are given a ruler beneath the wave.

#### a. Wavelength:
- Measure the distance between two consecutive crests or troughs.
- First crest starts around 0 cm, next crest at ~4 cm, then ~8 cm, then ~12 cm.
- So, one full wavelength = 4 cm

✔ Wavelength: 4 cm

#### b. Amplitude:
- The vertical distance from the equilibrium line (center) to the crest.
- On the vertical scale, the wave peaks at about 1 cm above the center line.

✔ Amplitude: 1 cm

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3. How many nodes and antinodes are in each of these diagrams?

These are standing wave patterns.

#### Left Diagram:
- It shows two loops (one full wavelength).
- Nodes: Points where the wave doesn't move (at ends and middle).
- There are 3 nodes (at both ends and one in the center).
- Antinodes: Points of maximum amplitude (peaks and troughs).
- There are 2 antinodes (one at each peak).

✔ Left:
- Nodes: 3
- Antinodes: 2

#### Right Diagram:
- More complex pattern — looks like 5 loops (i.e., 5 half-waves), so it's the 5th harmonic.
- Each loop has a node at each end and an antinode in the middle.
- Number of nodes = number of loops + 1 = 6
- Number of antinodes = number of loops = 5

✔ Right:
- Nodes: 6
- Antinodes: 5

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4. True or False: Constructive interference occurs when a crest meets up with another crest at a given location along the medium.

Yes! When two crests meet, they add together → larger amplitude → constructive interference.

✔ Answer: TRUE

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5. True or False: Destructive interference occurs when a trough meets up with another trough at a given location along the medium.

No! When two troughs meet, they also add together → larger negative displacement → still constructive interference (just downward).

Destructive interference happens when a crest meets a trough.

So this statement is False.

✔ Answer: FALSE

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6. Determine whether the following diagram will produce constructive, destructive, or complete destructive interference, and explain why. What is the height of the resulting amplitude?

The diagram shows:

- Two waves approaching each other.
- Both are crests (upward humps).
- They are identical in shape and size.
- They are moving toward each other and will meet at the center.

When two equal crests meet, they add together → constructive interference.

The resulting wave will have an amplitude equal to the sum of the individual amplitudes.

Assuming each wave has an amplitude of 1 unit (from the grid), the combined amplitude will be:

> 1 + 1 = 2 units

So:
- Type of interference: Constructive
- Resulting amplitude: 2 units

✔ Answer:
- Constructive interference
- Because two crests meet, adding their displacements.
- The resulting amplitude is 2 units.

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✔ Final Answers Summary:

1. Wavelength: A, Amplitude: B
2. a. Wavelength: 4 cm
b. Amplitude: 1 cm
3. Left: Nodes: 3, Antinodes: 2
Right: Nodes: 6, Antinodes: 5
4. True
5. False
6. Constructive interference – because two crests meet and add. Resulting amplitude: 2 units

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