3. The measurements for one sine wave of water are showed below. Find the period T, wavelength 2, frequency, and speed of this wave. 1s Time Water Le Water Level at Center 1 2 3 4 7 8 10 Position (cm) Water Level Water Level
3. The measurements for one sine wave of water are showed below. Find the period T, wavelength 2, frequency, and speed of this wave. 1s Time Water Le Water Level at Center 1 2 3 4 7 8 10 Position (cm) Water Level Water Level
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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### Wave Measurements and Analysis
**Problem 3**: The measurements for one sine wave of water are shown below. Find the period (T), wavelength (λ), frequency (f), and speed (v) of this wave.
**Diagrams and Graphs Explanation**
#### Diagram 1: Sine Wave of Water Over Time
- **Y-Axis**: Water Level
- **X-Axis**: Time in seconds (s)
- **Graph Description**: This graph demonstrates the water level fluctuating over a period of time, depicting a sine wave pattern. The cycle of the wave completes over a time period of 1 second, indicating the period (T) is 1 second.
#### Diagram 2: Water Level at Center Over Position
- **Y-Axis**: Water Level
- **X-Axis**: Position in centimeters (cm)
- **Graph Description**: This graph shows the water level varying along different positions measured in centimeters. The wavelength (λ), which is the distance between successive crests or troughs, can be observed from this spatial graph.
**Calculations and Analysis**
1. **Period (T)**:
- From Diagram 1, the period (T) of the sine wave is 1 second as each complete wave cycle takes 1 second.
2. **Wavelength (λ)**:
- In Diagram 2, the wavelength (λ) can be determined by measuring the distance between two successive points that are in phase (e.g., crest to crest or trough to trough). Observing the graph, the wavelength (λ) is approximately 6 cm.
3. **Frequency (f)**:
- Frequency is the reciprocal of the period.
- \(f = \frac{1}{T}\)
- Given \(T = 1 \text{s}\),
\[
f = \frac{1}{1 \text{s}} = 1 \text{Hz}
\]
4. **Speed (v)**:
- The wave speed can be calculated using the formula \(v = f \lambda\).
- Given \(f = 1 \text{Hz}\) and \(\lambda = 6 \text{cm}\),
\[
v = 1 \text{Hz} \times 6 \text{cm} = 6 \text{cm/s}
\]
By analyzing the given graphs,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F37e1db01-06d0-4e20-aae1-26f96b6814c3%2F1263df46-7dfe-4df6-afc3-bbabdba43a06%2Fazyrsi_processed.png&w=3840&q=75)
Transcribed Image Text:---
### Wave Measurements and Analysis
**Problem 3**: The measurements for one sine wave of water are shown below. Find the period (T), wavelength (λ), frequency (f), and speed (v) of this wave.
**Diagrams and Graphs Explanation**
#### Diagram 1: Sine Wave of Water Over Time
- **Y-Axis**: Water Level
- **X-Axis**: Time in seconds (s)
- **Graph Description**: This graph demonstrates the water level fluctuating over a period of time, depicting a sine wave pattern. The cycle of the wave completes over a time period of 1 second, indicating the period (T) is 1 second.
#### Diagram 2: Water Level at Center Over Position
- **Y-Axis**: Water Level
- **X-Axis**: Position in centimeters (cm)
- **Graph Description**: This graph shows the water level varying along different positions measured in centimeters. The wavelength (λ), which is the distance between successive crests or troughs, can be observed from this spatial graph.
**Calculations and Analysis**
1. **Period (T)**:
- From Diagram 1, the period (T) of the sine wave is 1 second as each complete wave cycle takes 1 second.
2. **Wavelength (λ)**:
- In Diagram 2, the wavelength (λ) can be determined by measuring the distance between two successive points that are in phase (e.g., crest to crest or trough to trough). Observing the graph, the wavelength (λ) is approximately 6 cm.
3. **Frequency (f)**:
- Frequency is the reciprocal of the period.
- \(f = \frac{1}{T}\)
- Given \(T = 1 \text{s}\),
\[
f = \frac{1}{1 \text{s}} = 1 \text{Hz}
\]
4. **Speed (v)**:
- The wave speed can be calculated using the formula \(v = f \lambda\).
- Given \(f = 1 \text{Hz}\) and \(\lambda = 6 \text{cm}\),
\[
v = 1 \text{Hz} \times 6 \text{cm} = 6 \text{cm/s}
\]
By analyzing the given graphs,
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