30+ Free Printable Waves Worksheets With Answer Key - Free Printable

To solve the problems in the worksheet, we need to analyze each wave diagram and use the definitions provided for amplitude, wavelength, frequency, and speed. Let's go through each wave step by step.

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Wave 1

#### a) How many wave cycles are completed in this diagram?
- From the diagram, we can see that there are 5 complete wave cycles in the given time (1 second).

#### b) Wavelength (λ)
- The wavelength is the distance between two consecutive crests or troughs.
- Measure the distance between two identical points on consecutive waves.
- From the diagram, the wavelength appears to be approximately 2 cm.

#### c) Amplitude (A)
- The amplitude is the height of the wave from the equilibrium position to the top of a crest or the bottom of a trough.
- Measure the vertical distance from the equilibrium line to the crest.
- From the diagram, the amplitude appears to be approximately 1 cm.

#### d) Frequency (f)
- Frequency is the number of waves that pass a point in a given amount of time.
- Since there are 5 complete cycles in 1 second, the frequency is:
\[
f = \frac{\text{Number of cycles}}{\text{Time}} = \frac{5}{1} = 5 \, \text{Hz}
\]

#### e) Speed (v)
- Speed is calculated using the formula:
\[
v = \text{wavelength} \times \text{frequency}
\]
- Substituting the values:
\[
v = \lambda \times f = 2 \, \text{cm} \times 5 \, \text{Hz} = 10 \, \text{cm/s}
\]

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Wave 2

#### a) How many wave cycles are completed in this diagram?
- From the diagram, we can see that there are 8 complete wave cycles in the given time (1 second).

#### b) Wavelength (λ)
- Measure the distance between two consecutive crests or troughs.
- From the diagram, the wavelength appears to be approximately 1.25 cm.

#### c) Amplitude (A)
- Measure the vertical distance from the equilibrium line to the crest.
- From the diagram, the amplitude appears to be approximately 0.5 cm.

#### d) Frequency (f)
- Since there are 8 complete cycles in 1 second, the frequency is:
\[
f = \frac{\text{Number of cycles}}{\text{Time}} = \frac{8}{1} = 8 \, \text{Hz}
\]

#### e) Speed (v)
- Using the formula \( v = \lambda \times f \):
\[
v = 1.25 \, \text{cm} \times 8 \, \text{Hz} = 10 \, \text{cm/s}
\]

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Wave 3

#### a) How many wave cycles are completed in this diagram?
- From the diagram, we can see that there are 2 complete wave cycles in the given time (1 second).

#### b) Wavelength (λ)
- Measure the distance between two consecutive crests or troughs.
- From the diagram, the wavelength appears to be approximately 4 cm.

#### c) Amplitude (A)
- Measure the vertical distance from the equilibrium line to the crest.
- From the diagram, the amplitude appears to be approximately 2 cm.

#### d) Frequency (f)
- Since there are 2 complete cycles in 1 second, the frequency is:
\[
f = \frac{\text{Number of cycles}}{\text{Time}} = \frac{2}{1} = 2 \, \text{Hz}
\]

#### e) Speed (v)
- Using the formula \( v = \lambda \times f \):
\[
v = 4 \, \text{cm} \times 2 \, \text{Hz} = 8 \, \text{cm/s}
\]

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Wave 4

#### a) How many wave cycles are completed in this diagram?
- From the diagram, we can see that there are 6 complete wave cycles in the given time (1 second).

#### b) Wavelength (λ)
- Measure the distance between two consecutive crests or troughs.
- From the diagram, the wavelength appears to be approximately 1.67 cm.

#### c) Amplitude (A)
- Measure the vertical distance from the equilibrium line to the crest.
- From the diagram, the amplitude appears to be approximately 0.5 cm.

#### d) Frequency (f)
- Since there are 6 complete cycles in 1 second, the frequency is:
\[
f = \frac{\text{Number of cycles}}{\text{Time}} = \frac{6}{1} = 6 \, \text{Hz}
\]

#### e) Speed (v)
- Using the formula \( v = \lambda \times f \):
\[
v = 1.67 \, \text{cm} \times 6 \, \text{Hz} \approx 10 \, \text{cm/s}
\]

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Final Answers

1. Wave 1:
- a) 5
- b) 2 cm
- c) 1 cm
- d) 5 Hz
- e) 10 cm/s

2. Wave 2:
- a) 8
- b) 1.25 cm
- c) 0.5 cm
- d) 8 Hz
- e) 10 cm/s

3. Wave 3:
- a) 2
- b) 4 cm
- c) 2 cm
- d) 2 Hz
- e) 8 cm/s

4. Wave 4:
- a) 6
- b) 1.67 cm
- c) 0.5 cm
- d) 6 Hz
- e) 10 cm/s

\boxed{
\begin{array}{l}
\text{Wave 1: } 5, 2 \, \text{cm}, 1 \, \text{cm}, 5 \, \text{Hz}, 10 \, \text{cm/s} \\
\text{Wave 2: } 8, 1.25 \, \text{cm}, 0.5 \, \text{cm}, 8 \, \text{Hz}, 10 \, \text{cm/s} \\
\text{Wave 3: } 2, 4 \, \text{cm}, 2 \, \text{cm}, 2 \, \text{Hz}, 8 \, \text{cm/s} \\
\text{Wave 4: } 6, 1.67 \, \text{cm}, 0.5 \, \text{cm}, 6 \, \text{Hz}, 10 \, \text{cm/s}
\end{array}
}