Wave diagrams illustrating amplitude, wavelength, frequency, and speed with related questions.

To solve the problems in the worksheet, we need to analyze the provided wave diagrams and use the definitions of amplitude, wavelength, frequency, and speed. Let's break it down step by step for both waves.

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Wave 1

#### a) How many wave cycles are completed in this diagram?
- A wave cycle is defined as one complete oscillation from a crest to a trough and back to a crest.
- Count the number of complete cycles in the diagram:
- There are 5 complete wave cycles in the diagram.

#### b) Wavelength (λ) in cm
- The wavelength is the horizontal distance between two consecutive crests or troughs.
- Measure the distance between two consecutive crests or troughs in the diagram:
- Assume the scale is such that each division represents 1 cm.
- From the diagram, the wavelength appears to be 2 cm.

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

#### d) Frequency (f) in Hz
- Frequency is the number of wave cycles completed per second.
- According to the problem, 1 second is the time for the wave to complete its cycles.
- Since there are 5 complete cycles in 1 second:
\[
f = \frac{\text{Number of cycles}}{\text{Time}} = \frac{5}{1} = 5 \, \text{Hz}
\]

#### e) Speed (v) in cm/s
- The speed of a wave is given by the formula:
\[
v = \lambda \times f
\]
- Substitute the values:
\[
v = 2 \, \text{cm} \times 5 \, \text{Hz} = 10 \, \text{cm/s}
\]

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Wave 2

#### a) How many wave cycles are completed in this diagram?
- Count the number of complete cycles in the diagram:
- There are 8 complete wave cycles in the diagram.

#### b) Wavelength (λ) in cm
- Measure the horizontal distance between two consecutive crests or troughs:
- From the diagram, the wavelength appears to be 1.5 cm.

#### c) Amplitude (A) in cm
- Measure the vertical distance from the middle line to the top of a crest:
- From the diagram, the amplitude appears to be 0.5 cm.

#### d) Frequency (f) in Hz
- According to the problem, 1 second is the time for the wave to complete its cycles.
- Since there are 8 complete cycles in 1 second:
\[
f = \frac{\text{Number of cycles}}{\text{Time}} = \frac{8}{1} = 8 \, \text{Hz}
\]

#### e) Speed (v) in cm/s
- Use the formula for wave speed:
\[
v = \lambda \times f
\]
- Substitute the values:
\[
v = 1.5 \, \text{cm} \times 8 \, \text{Hz} = 12 \, \text{cm/s}
\]

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Final Answers

#### Wave 1
a) Number of wave cycles: 5
b) Wavelength: 2 cm
c) Amplitude: 1 cm
d) Frequency: 5 Hz
e) Speed: 10 cm/s

#### Wave 2
a) Number of wave cycles: 8
b) Wavelength: 1.5 cm
c) Amplitude: 0.5 cm
d) Frequency: 8 Hz
e) Speed: 12 cm/s

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Boxed Final Answers

\[
\boxed{
\begin{array}{ll}
\text{Wave 1:} & \\
\text{a)} & 5 \\
\text{b)} & 2 \, \text{cm} \\
\text{c)} & 1 \, \text{cm} \\
\text{d)} & 5 \, \text{Hz} \\
\text{e)} & 10 \, \text{cm/s} \\
\hline
\text{Wave 2:} & \\
\text{a)} & 8 \\
\text{b)} & 1.5 \, \text{cm} \\
\text{c)} & 0.5 \, \text{cm} \\
\text{d)} & 8 \, \text{Hz} \\
\text{e)} & 12 \, \text{cm/s} \\
\end{array}
}
\]