Textbook Question
A transverse wave with a frequency of 220 Hz and a wavelength of 10.0 cm is traveling along a cord. The maximum speed of particles on the cord is 0.10 the wave speed. What is the amplitude of the wave?
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Ch. 15 - Wave Motion
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179
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Table of contents
- Ch. 01 - Introduction, Measurement, Estimating10
- Ch. 02 - Describing Motion: Kinematics in One Dimension30
- Ch. 03 - Kinematics in Two or Three Dimensions; Vectors15
- Ch. 04 - Dynamics: Newton's Laws of Motion16
- Ch. 05 - Using Newton's Laws: Friction, Circular Motion, Drag Forces22
- Ch. 06 - Gravitation and Newton's Synthesis10
- Ch. 07 - Work and Energy21
- Ch. 08 - Conservation of Energy33
- Ch. 09 - Linear Momentum26
- Ch. 10 - Rotational Motion41
- Ch. 11 - Angular Momentum; General Rotation27
- Ch. 12 - Static Equilibrium; Elasticity and Fracture27
- Ch. 13 - Fluids28
- Ch. 14 - Oscillations14
- Ch. 15 - Wave Motion35
- Ch. 16 - Sound5
- Ch. 17 - Temperature, Thermal Expansion, and the Ideal Gas Law40
- Ch. 18 - Kinetic Theory of Gases18
- Ch. 19 - Heat and the First Law of Thermodynamics31
- Ch. 20 - Second Law of Thermodynamics32
- Ch. 21 - Electric Charge and Electric Field7
- Ch. 23 - Electric Potential20
- Ch. 24 - Capacitance, Dielectrics, Electric Energy, Storage15
- Ch. 25 - Electric Current and Resistance32
- Ch. 26 - DC Circuits22
- Ch. 27 - Magnetism21
- Ch. 28 - Sources of Magnetic Field24
- Ch. 29 - Electromagnetic Induction and Faraday's Law21
- Ch. 30 - Inductance, Electromagnetic Oscillations, and AC Circuits42
- Ch. 31 - Maxwell's Equations and Electromagnetic Waves25
- Ch. 32 - Light: Reflection and Refraction42
- Ch. 33 - Lenses and Optical Instruments21
- Ch. 34 - The Wave Nature of Light: Interference and Polarization26
- Ch. 35 - Diffraction24
- Ch. 36 - The Special Theory of Relativity29
- Ch. 38 - Quantum Mechanics1
- Ch. 40 - Molecules and Solids6
- Ch. 43 - Elementary Particles3
- Ch. 44 - Astrophysics and Cosmology9
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook
Chapter 15, Problem 29b
A 572-Hz longitudinal wave in air has a speed of 345 m/s. How much time is required for the phase to change by 90° at a given point in space?
Verified step by step guidance1
Determine the period of the wave using the formula for the period: , where is the frequency of the wave (572 Hz).
Recognize that a phase change of 90° corresponds to one-quarter of a full cycle, as a full cycle corresponds to 360°.
Calculate the time required for a 90° phase change by taking one-quarter of the period: .
Substitute the value of the period (calculated in step 1) into the equation from step 3 to find the time for the phase change.
Express the final result in seconds, ensuring the units are consistent throughout the calculation.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Wave Speed
Wave speed is the rate at which a wave propagates through a medium. It is determined by the medium's properties and can be calculated using the formula v = fλ, where v is the wave speed, f is the frequency, and λ is the wavelength. In this case, the wave speed is given as 345 m/s.
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Intro to Waves and Wave Speed
Frequency
Frequency is the number of cycles of a wave that pass a given point per unit time, measured in hertz (Hz). For the given wave, the frequency is 572 Hz, indicating that 572 cycles occur every second. This concept is crucial for understanding how quickly the wave oscillates and relates directly to the time it takes for phase changes.
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Phase Change
Phase change in a wave refers to the shift in the wave's position in its cycle, typically measured in degrees or radians. A 90° phase change corresponds to a quarter of a wavelength. To find the time required for this phase change, one can use the relationship between frequency and time, where time is the inverse of frequency, allowing for the calculation of the duration for a specific phase shift.
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Related Practice
Textbook Question
A 572-Hz longitudinal wave in air has a speed of 345 m/s. At a particular instant, what is the phase difference (in degrees) between two points 4.4 cm apart?
Textbook Question
A 572-Hz longitudinal wave in air has a speed of 345 m/s. What is the wavelength?
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Textbook Question
Write the equation for the wave in Problem 29 traveling to the right, if its amplitude is 0.020 cm, and D = - 0.020 cm, at t = 0 and x = 0.
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Textbook Question
A transverse wave on a cord is given by D(x,t) = 0.12 sin (3.0x - 15.0t), where D and x are in meters and t is in seconds. At t = 0.20s, what are the displacement, velocity, and acceleration of a point on the cord where x = 0.60 m?
Textbook Question
A transverse wave pulse travels to the right along a string with a speed v = 2.0 m/s. At the shape of the pulse is given by the function D = 0.45 cos (2.6x + 1.2), where D and x are in meters. Determine a formula for the wave pulse at any time t assuming there are no frictional losses.
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