### Understanding Wave Motion in a Slinky SpringIn this lesson, we will explore the concept of wave motion using a stretched-out Slinky spring. Consider the following scenario:A stretched-out Slinky spring is shaken rapidly, completing 4 up-and-down shakes every second. A photograph of the Slinky reveals that the distance between consecutive wave crests (the wavelength) is 0.72 meters. We want to determine the velocity of the wave moving along the Slinky.#### Key Information:- **Frequency (f)**: 4 Hz (4 shakes per second)- **Wavelength (λ)**: 0.72 meters#### Formula for Wave Velocity:To calculate the wave velocity (v), we use the equation:\[ v = f \lambda \]Where:- \( v \) is the speed or velocity of the wave (meters per second, ms⁻¹)- \( f \) is the frequency (Hertz, Hz)- \( \lambda \) is the wavelength (meters, m)#### Diagram Explanation:The provided diagram visually represents the formula \( v = f \lambda \) with arrows pointing to each variable:- **Speed or Velocity (v)** is indicated in green (ms⁻¹).- **Frequency (f)** is indicated in blue (Hz).- **Wavelength (λ)** is indicated in red (meters, m).#### Calculation:By substituting the given values into the formula, we find:\[ v = 4 \, \text{Hz} \times 0.72 \, \text{m} = 2.88 \, \text{ms}⁻¹ \]Therefore, the velocity of the wave is **2.88 meters per second (ms⁻¹)**.#### Multiple Choice Question:The velocity of the wave is:- \( \square \) 4.72- \( \square \) 0.18- \( \square \) 2.88 (Correct Answer)- \( \square \) 3.24

Given data: Frequency (f) = 4 Hz Wavelength (λ) = 0.72 m Required: Velocity (v)

A stretched-out Slinky spring is shaken rapidly (4 complete up-and-down shakes per second). A photograph reveals the wave crests are 0.72 meters apart. The ripple move along the Slinky with a velocity of meters/second. (use the equation shown below to help you calculate the answer) speed or velocity (ms ¹) v=fλ= frequency (Hz) 4.72 O 0.18 2.88 3.24 wavelength (m)

A stretched-out Slinky spring is shaken rapidly (4 complete up-and-down shakes per second). A photograph reveals the wave crests are 0.72 meters apart. The ripple move along the Slinky with a velocity of meters/second. (use the equation shown below to help you calculate the answer) speed or velocity (ms ¹) v=fλ= frequency (Hz) 4.72 O 0.18 2.88 3.24 wavelength (m)

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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Interference of sound

Seiche

A seiche is an oscillating standing wave in a body of water. The term seiche pronounced saysh) can be understood by the sloshing of water back and forth in a swimming pool. The same phenomenon happens on a much larger scale in vast bodies of water including bays and lakes. A seizure can happen in any enclosed or semi-enclosed body of water.

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### Understanding Wave Motion in a Slinky Spring

In this lesson, we will explore the concept of wave motion using a stretched-out Slinky spring. Consider the following scenario:

A stretched-out Slinky spring is shaken rapidly, completing 4 up-and-down shakes every second. A photograph of the Slinky reveals that the distance between consecutive wave crests (the wavelength) is 0.72 meters. We want to determine the velocity of the wave moving along the Slinky.

#### Key Information:
- **Frequency (f)**: 4 Hz (4 shakes per second)
- **Wavelength (λ)**: 0.72 meters

#### Formula for Wave Velocity:
To calculate the wave velocity (v), we use the equation:

\[ v = f \lambda \]

Where:
- \( v \) is the speed or velocity of the wave (meters per second, ms⁻¹)
- \( f \) is the frequency (Hertz, Hz)
- \( \lambda \) is the wavelength (meters, m)

#### Diagram Explanation:
The provided diagram visually represents the formula \( v = f \lambda \) with arrows pointing to each variable:
- **Speed or Velocity (v)** is indicated in green (ms⁻¹).
- **Frequency (f)** is indicated in blue (Hz).
- **Wavelength (λ)** is indicated in red (meters, m).

#### Calculation:
By substituting the given values into the formula, we find:

\[ v = 4 \, \text{Hz} \times 0.72 \, \text{m} = 2.88 \, \text{ms}⁻¹ \]

Therefore, the velocity of the wave is **2.88 meters per second (ms⁻¹)**.

#### Multiple Choice Question:
The velocity of the wave is:
- \( \square \) 4.72
- \( \square \) 0.18
- \( \square \) 2.88 (Correct Answer)
- \( \square \) 3.24

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