### Understanding Wave Frequency and PeriodWhen studying waves, such as those traveling through a slinky, it's essential to understand the relationship between the wave's frequency and its period. #### Question 1:Changing the period of a wave going through a slinky will cause different frequencies. What would be the relationship between frequency and period?#### Multiple Choice Options:- **Linear proportional**- **Inverse**- **Linear horizontal**- **Quadratic**- **Inverse squared**When changing the period \( T \) of a wave, you directly affect the frequency \( f \). The relationship between period and frequency is typically inverse, meaning as the period increases, the frequency decreases, and vice versa. This inverse relationship can be described mathematically by:\[ f = \frac{1}{T} \]By understanding this principle, it enables us to predict how a wave's frequency will change in response to modifications in its period. This fundamental concept is critical in various fields, from physics to engineering, and can be observed in both mechanical waves, like those in a slinky, and electromagnetic waves. ### Understanding the Relationship Between Frequency and Wavelength#### Problem StatementShaking a slinky with a wave speed of 250 m/s at different frequencies will show what kind of relationship between frequency and wavelength.---#### Graph AnalysisTo determine the kind of relationship between frequency and wavelength, let's consider the following graphs:1. **Graph 1:** - **Description:** This graph shows an upward curve starting from the lower left corner and rising steeply towards the upper right corner. - **Interpretation:** This suggests an exponential increase in wavelength with increasing frequency, which does not typically align with the known wave equation relationship.2. **Graph 2:** - **Description:** This graph shows a constant straight line parallel to the x-axis. - **Interpretation:** This implies that the wavelength remains constant irrespective of the frequency, which is incorrect according to wave theory.3. **Graph 3:** - **Description:** This graph displays a straight-line increase from the bottom left to the top right. - **Interpretation:** This suggests a direct linear relationship between frequency and wavelength, which is not characteristic of wave behavior.4. **Graph 4:** - **Description:** This graph shows a downward curve that starts at the top left and descends to the bottom right. - **Interpretation:** This graph suggests an inverse relationship between frequency and wavelength, which is consistent with the wave equation \((\text{Wavelength} = \text{Wave speed} / \text{Frequency})\).#### Correct InterpretationConsidering the wave equation \(\text{Wavelength} = \frac{\text{Wave speed}}{\text{Frequency}}\), the relationship between frequency and wavelength is inverse. As the frequency of the wave increases, the wavelength decreases. **Correct Graph:** The fourth graph represents this inverse relationship correctly.### SummaryWhen shaking a slinky with a wave speed of 250 m/s, an inverse relationship between frequency and wavelength is observed. This means that higher frequencies result in shorter wavelengths. This principle is consistent with the fundamental wave equation highlighting the relationship among wave speed, frequency, and wavelength.

Given question based on frequency and wavelength relation

1 Changing the period of a wave going through a slinky will cause different frequencies. What would be the relationship between frequency and period? 1 Linear proportional Inverse Linear horizontal quadratic Inverse squared

1 Changing the period of a wave going through a slinky will cause different frequencies. What would be the relationship between frequency and period? 1 Linear proportional Inverse Linear horizontal quadratic Inverse squared

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

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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