Textbook Question
What is the frequency of an electromagnetic wave that has the same wavelength as a 2.5 kHz sound wave in water?
Ch 16: Traveling Waves
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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Table of contents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
Chapter 16, Problem 8
FIGURE EX16.8 is a picture at t = 0 s of the particles in a medium as a longitudinal wave is passing through. The equilibrium spacing between the particles is 1.0 cm. Draw the snapshot graph D(x, t = 0 s) of this wave at t = 0 s.
Verified step by step guidance1
Step 1: Observe the image provided. The red squares represent particles in a medium, and their positions indicate the compression and rarefaction regions of a longitudinal wave. The equilibrium spacing between particles is 1.0 cm.
Step 2: Identify the regions of compression and rarefaction. Compression occurs where particles are closer together than the equilibrium spacing, and rarefaction occurs where particles are farther apart than the equilibrium spacing.
Step 3: To draw the snapshot graph D(x, t = 0 s), plot the displacement of particles (D) as a function of position (x). Displacement is positive for particles displaced to the right of their equilibrium position and negative for particles displaced to the left.
Step 4: Analyze the positions of the particles in the image. For example, at x = 16 cm, particles are compressed, indicating a peak in the graph. At x = 10 cm, particles are rarefied, indicating a trough in the graph.
Step 5: Sketch the graph by connecting the peaks and troughs smoothly to represent the wave. Ensure the graph reflects the periodic nature of the wave, with alternating regions of compression and rarefaction.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Longitudinal Waves
Longitudinal waves are a type of mechanical wave where the particle displacement is parallel to the direction of wave propagation. In these waves, particles in the medium oscillate back and forth along the same line as the wave travels, creating regions of compression and rarefaction. This is in contrast to transverse waves, where particle displacement is perpendicular to wave direction.
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Equilibrium Spacing
Equilibrium spacing refers to the natural distance between particles in a medium when no wave is passing through. In the context of longitudinal waves, this spacing is crucial for understanding how particles compress and expand as the wave moves. The given equilibrium spacing of 1.0 cm indicates the distance between adjacent particles when they are at rest, which helps in visualizing the wave's effect on the medium.
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Snapshot Graph
A snapshot graph represents the position of particles in a medium at a specific moment in time, illustrating the wave's effect. For longitudinal waves, this graph typically shows the compressions and rarefactions of particles along the medium. At t = 0 s, the graph will depict the arrangement of particles based on their displacement from the equilibrium position, allowing for a visual understanding of the wave's characteristics.
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Related Practice
Textbook Question
Show that the displacement D(x,t) = ln(ax + bt), where a and b are constants, is a solution to the wave equation. Then find an expression in terms of a and b for the wave speed.
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Textbook Question
The wave speed on a string under tension is 200 m/s. What is the speed if the tension is halved?
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Textbook Question
Show that the displacement D(x,t) = cx² + dt², where c and d are constants, is a solution to the wave equation. Then find an expression in terms of c and d for the wave speed.
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Textbook Question
Draw the history graph D(x = 4.0 m, t) at x = 4.0 m for the wave shown in FIGURE EX16.4.
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