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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![**Understanding Waves**
**What is a wave?**
A wave is a disturbance that travels through a medium, transferring energy from one point to another without causing any permanent displacement of the medium itself. Waves are characterized by their wavelength, frequency, amplitude, and speed.
**What is the difference between wave motion and particle motion?**
The primary difference is that in wave motion, energy is transferred through the medium without transferring matter. In particle motion, particles of the medium move from one place to another, resulting in energy transfer and displacement of matter.
**What are the characteristics of mechanical waves?**
Mechanical waves require a medium to travel through and are governed by the principles of motion in that medium. Characteristics include:
- **Wavelength (\(\lambda\))**: The distance between successive crests or troughs of the wave.
- **Frequency (f)**: The number of wave cycles that pass a given point in one second.
- **Amplitude (A)**: The maximum displacement of points on the wave, which relates to the wave's energy.
- **Speed (v)**: The rate at which the wave propagates through the medium.
**Sine Waves and Sinusoidal Waves**
**What is a sine wave or sinusoidal wave?**
A sine wave is a mathematical curve that describes a smooth, periodic oscillation. It is often characterized by its repetitive pattern, which makes it fundamental in various fields such as physics, engineering, and signal processing.
**Write the general form of a sine wave and define each term.**
The general form of a sine wave is given by:
\[ y(x, t) = A \sin(kx - \omega t + \phi) \]
where:
- \(A\): Amplitude of the wave
- \(k\): Wave number, related to the wavelength by \(k = \frac{2\pi}{\lambda}\)
- \(\omega\): Angular frequency, related to the frequency by \(\omega = 2\pi f\)
- \(\phi\): Phase constant, which determines the wave's position at \(t = 0\)
- \(x\): Position along the medium
- \(t\): Time
**Example Problem:**
Given the wave function \( y(x, t) = 0.150 \sin(20x - 60t) \) m, find the frequency and speed of this wave.
**Solution:**
- The amplitude \( A \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F37e1db01-06d0-4e20-aae1-26f96b6814c3%2F5b00c6e9-5d7e-4404-940d-9a12bf695b59%2F2cgthnu_processed.png&w=3840&q=75)
Transcribed Image Text:**Understanding Waves**
**What is a wave?**
A wave is a disturbance that travels through a medium, transferring energy from one point to another without causing any permanent displacement of the medium itself. Waves are characterized by their wavelength, frequency, amplitude, and speed.
**What is the difference between wave motion and particle motion?**
The primary difference is that in wave motion, energy is transferred through the medium without transferring matter. In particle motion, particles of the medium move from one place to another, resulting in energy transfer and displacement of matter.
**What are the characteristics of mechanical waves?**
Mechanical waves require a medium to travel through and are governed by the principles of motion in that medium. Characteristics include:
- **Wavelength (\(\lambda\))**: The distance between successive crests or troughs of the wave.
- **Frequency (f)**: The number of wave cycles that pass a given point in one second.
- **Amplitude (A)**: The maximum displacement of points on the wave, which relates to the wave's energy.
- **Speed (v)**: The rate at which the wave propagates through the medium.
**Sine Waves and Sinusoidal Waves**
**What is a sine wave or sinusoidal wave?**
A sine wave is a mathematical curve that describes a smooth, periodic oscillation. It is often characterized by its repetitive pattern, which makes it fundamental in various fields such as physics, engineering, and signal processing.
**Write the general form of a sine wave and define each term.**
The general form of a sine wave is given by:
\[ y(x, t) = A \sin(kx - \omega t + \phi) \]
where:
- \(A\): Amplitude of the wave
- \(k\): Wave number, related to the wavelength by \(k = \frac{2\pi}{\lambda}\)
- \(\omega\): Angular frequency, related to the frequency by \(\omega = 2\pi f\)
- \(\phi\): Phase constant, which determines the wave's position at \(t = 0\)
- \(x\): Position along the medium
- \(t\): Time
**Example Problem:**
Given the wave function \( y(x, t) = 0.150 \sin(20x - 60t) \) m, find the frequency and speed of this wave.
**Solution:**
- The amplitude \( A \
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