The drawings represent snapshots taken of waves traveling to the right along strings. The grids shown in the background are identical. The waves all have the same speed, but their amplitudes vary. A B M Rank the wavelength of the waves (greatest to least). Explain your reasoning. C D

The drawings represent snapshots taken of waves traveling to the right along strings. The grids shown in the background are identical. The waves all have the same speed, but their amplitudes vary. A B M Rank the wavelength of the waves (greatest to least). Explain your reasoning. C D

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter1: Getting Started

Section: Chapter Questions

Problem 52PQ: Later in this book, you will learn that sound is a wave. The wavelength and frequency f of a wave...

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Concept explainers

Wave Motion

A wave motion is defined as the propagation of disturbances or transfer of energy and momentum from the state of rest or equilibrium to another point in a medium without any actual transfer of matter between them. In a simple explanation, it is the propagation of energy through a medium that is produced due to the repeated vibrations of the particles. Common things we see day to day like waves on water oscillation of a pendulum or bell, light wave, and all the subatomic particles exhibiting wavelike properties. The propagation of waves depends on the medium and their properties. The wave function is the disturbance that produces waves as a function of time. This disturbance oscillates periodically with a fixed frequency and wavelength. There are linear wave motion and non-linear wave motion based on their propagation, motion, and time period where linear wave motion is like sinusoidal waves and non-linear wave motion like a wave motion that gets interrupted in the middle of their propagation.

Question

### Understanding Wave Wavelengths

The drawings represent snapshots taken of waves traveling to the right along strings. The grids shown in the background are identical. The waves all have the same speed, but their amplitudes vary.

#### Wave Diagrams:

- **Diagram A:**
- Wave with moderate amplitude and frequency.
- The wave completes two full cycles within the given grid.

- **Diagram B:**
- Wave with higher amplitude and higher frequency.
- The wave completes nearly three full cycles within the given grid.

- **Diagram C:**
- Wave with the smallest amplitude and lowest frequency.
- The wave completes less than one full cycle within the given grid.

- **Diagram D:**
- Wave with moderate amplitude but lower frequency compared to A and B.
- The wave completes just over one full cycle within the given grid.

### Task:
Rank the wavelength of the waves (greatest to least). Explain your reasoning.

#### Explanation:
- **Wavelength** is the distance between successive crests (or troughs) of a wave.
- A longer wavelength means fewer cycles within the same distance, indicating a lower frequency.

**Ranking the wavelengths from greatest to least:**
1. **Diagram C:** The longest wavelength as it completes the least number of cycles (less than one full cycle) within the grid.
2. **Diagram D:** The second-longest wavelength, completing just over one full cycle within the grid.
3. **Diagram A:** The third-longest wavelength, completing two full cycles within the grid.
4. **Diagram B:** The shortest wavelength, completing nearly three full cycles within the grid.

This ranking is based on the number of wave cycles observed in each diagram, with fewer cycles correlating to a longer wavelength.

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